% % CCA Bibliography on % Constructivity, Computability and Complexity in Analysis % % http://cca-net.de % % (c) 2000-2008 Vasco Brattka % @Article{AAFHS99, author = {Aps{\={\i}}tis, Kalvis and Arikawa, Setsuo and Freivalds, R{\=u}si{\c{n}}{\v{s}} and Hirowatari, Eiju and Smith, Carl H.}, title = {On the inductive inference of recursive real-valued functions}, journal = {Theoretical Computer Science}, year = {1999}, volume = {219}, pages = {3--17} } @Article{ABH08, author = {Archibald, Margaret and Brattka, Vasco and Heuberger, Clemens}, title = {Randomness with respect to the Signed-Digit Representation}, journal = {Fundamenta Informaticae}, year = {2008}, volume = {83}, number = {1--2}, pages = {1--19} } @InProceedings{AI05, author = {Akama, Yohji and Iizuka, Shinji}, title = {Real number representations of graph-directed {IFS} attractors}, booktitle = {Computability and Complexity in Analysis}, editor = {Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus}, year = {2005}, month = {July}, series = {Informatik Berichte}, volume = {326}, pages = {3--24}, publisher = {FernUniversit\"at in Hagen}, note = {Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25--29, 2005} } @Article{AS06, author = {Avigad, Jeremy and Simic, Ksenija}, title = {Fundamental notions of analysis in subsystems of second-order arithmetic}, journal = {Annals of Pure and Applied Logic}, year = {2006}, volume = {139}, pages = {138--184} } @Article{AWZ00, author = {Ambos-Spies, Klaus and Weihrauch, Klaus and Zheng, Xizhong}, title = {Weakly Computable Real Numbers}, journal = {Journal of Complexity}, year = {2000}, volume = {16}, number = {4}, pages = {676--690} } @Article{Abe68, author = {Aberth, Oliver}, title = {Analysis in the Computable Number Field}, journal = {Journal of the Association for Computing Machinery}, year = {1968}, volume = {15}, pages = {275--299} } @Article{Abe69, author = {Aberth, Oliver}, title = {A Chain of Inclusion Relations in Computable Analysis}, journal = {Proceedings of the American Mathematical Society}, year = {1969}, volume = {22}, pages = {539--548} } @InProceedings{Abe70, author = {Aberth, Oliver}, title = {Computable analysis and differential equations}, booktitle = {Intuitionism and Proof Theory}, editor = {Kino, A. and Myhill, J. and Vesley, R.E.}, year = {1970}, series = {Studies in Logic and the Foundations of Mathematics}, pages = {47--52}, publisher = {North-Holland}, address = {Amsterdam}, note = {Proc. of the Summer Conf. at Buffalo N.Y. 1968} } @Article{Abe71, author = {Aberth, Oliver}, title = {The failure in computable analysis of a classical existence theorem for differential equations}, journal = {Proceedings of the American Mathematical Society}, year = {1971}, volume = {30}, pages = {151--156} } @Book{Abe80, author = {Aberth, Oliver}, title = {Computable Analysis}, year = {1980}, publisher = {McGraw-Hill}, address = {New York} } @Article{Aka04, author = {Akama, Yohji}, title = {Limiting partial combinatory algebras}, journal = {Theoretical Computer Science}, year = {2004}, volume = {311}, pages = {199--220} } @TechReport{Amb98, author = {Ambos-Spies, Klaus}, title = {A Note on Recursively Approximable Real Numbers}, year = {1998}, number = {38}, type = {Forschungsbericht Mathematische Logik}, institution = {Universit\"at Heidelberg}, address = {Heidelberg} } @InProceedings{Avi05, author = {Avigad, Jeremy}, title = {Weak theories of nonstandard arithmetic and analysis}, booktitle = {Reverse Mathematics 2001}, editor = {Simpson, Stephen}, year = {2005}, series = {Lecture Notes in Logic}, pages = {19--46}, publisher = {Association for Symbolic Logic}, address = {La Jolla} } @Article{BA99, author = {Bedregal, Benjam{\'{\i}}n Ren{\'{e}} Callejas and Aci{\'{o}}ly, Benedito Melo}, title = {Effectively Given Continuous Domains: A Computable Interval Analysis}, journal = {Electronic Journal on Mathematics of Computation}, year = {1999}, volume = {0} } @Article{BB06, author = {Berger, Josef and Bridges, Douglas S.}, title = {A bizarre property equivalent to the {$\Pi^0_1$}--fan theorem}, journal = {Logic Journal of the IGPL}, year = {2006}, volume = {14}, pages = {867--871} } @Article{BB07, author = {Berger, Josef and Bridges, Douglas S.}, title = {A fan-theoretic equivalent of the antithesis of {S}pecker's theorem}, journal = {Indag. Math. N.S.}, year = {2007}, volume = {18}, number = {2}, pages = {195--202} } @InProceedings{BB08, author = {Baroni, M. A. and Bridges, D. S.}, title = {Continuity Properties of Preference Relations}, booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)}, editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning}, year = {2008}, series = {Electronic Notes in Theoretical Computer Science}, volume = {202}, pages = {19--25}, publisher = {Elsevier}, note = {CCA 2007, Siena, Italy, June 16--18, 2007} } @Article{BB08a, author = {Berger, Josef and Bridges, Douglas}, title = {The anti-{S}pecker property, a {H}eine–{B}orel property}, journal = {Archive for Mathematical Logic}, year = {2008}, volume = {46}, number = {7--8}, pages = {583–-592} } @Book{BB85, author = {Bishop, Errett and Bridges, Douglas S.}, title = {Constructive Analysis}, year = {1985}, series = {Grundlehren der Mathematischen Wissenschaften}, volume = {279}, publisher = {Springer}, address = {Berlin} } @Article{BBCRW08, author = {Barmpalias, George and Brodhead, Paul and Cenzer, Douglas and Remmel, Jeffrey B. and Weber, Rebecca}, title = {Algorithmic randomness of continuous functions}, journal = {Archive for Mathematical Logic}, year = {2008}, volume = {46}, number = {7--8}, pages = {533–-546} } @Article{BBGMV04, author = {Benci, V. and Bonanno, C. and Galatolo, S. and Menconi, G. and Virgilio, M.}, title = {Dynamical systems and computable information}, journal = {Discrete and Continuous Dynamical Systems B}, year = {2004}, volume = {4}, number = {4}, pages = {935--960} } @Proceedings{BBH01, title = {Computability and Complexity in Analysis}, editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter}, year = {2001}, series = {Lecture Notes in Computer Science}, volume = {2064}, publisher = {Springer}, address = {Berlin}, note = {4th International Workshop, CCA 2000, Swansea, UK, September 17-19, 2000. Selected Papers} } @Article{BBS04, author = {Bauer, Andrej and Birkedal, Lars and Scott, Dana S.}, title = {Equilogical spaces}, journal = {Theoretical Computer Science}, year = {2004}, volume = {315}, pages = {35--59} } @Article{BBS06, author = {Berger, Josef and Bridges, Douglas S. and Schuster, Peter}, title = {The fan theorem and unique existence of maxima}, journal = {The Journal of Symbolic Logic}, year = {2006}, volume = {71}, number = {2}, pages = {713--720} } @Article{BBY06, author = {Binder, I. and Braverman, Mark and Yampolsky, M.}, title = {On computational complexity of {S}iegel {J}ulia sets}, journal = {Comm. Math. Phys.}, year = {2006}, volume = {264}, number = {2}, pages = {317--334} } @Article{BC06, author = {Braverman, Mark and Cook, Stephen}, title = {Computing over the Reals: Foundations for Scientific Computing}, journal = {Notices of the AMS}, year = {2006}, volume = {53}, number = {3}, pages = {318--329} } @Article{BC08, author = {Brodhead, Paul and Cenzer, Douglas}, title = {Effectively closed sets and enumerations}, journal = {Archive for Mathematical Logic}, year = {2008}, volume = {46}, number = {7--8}, pages = {565–-582} } @Book{BC72, author = {Bishop, E. and Cheng, H.}, title = {Constructive {M}easure {T}heory}, year = {1972}, publisher = {American Mathematical Society}, address = {Providence} } @InProceedings{BC90, author = {Boehm, Hans and Cartwright, Robert}, title = {Exact real arithmetic, formulating real numbers as functions}, booktitle = {Research topics in functional programming}, editor = {Turner, D.}, year = {1990}, pages = {43--64}, publisher = {Addison-Wesley} } @InProceedings{BCD06, author = {Brodhead, Paul and Cenzer, Douglas and Dashti, Seyyed}, title = {Random Closed Sets}, booktitle = {Logical Approaches to Computational Barriers}, editor = {Beckmann, A. and Berger, U. and L{\"o}we, B. and Tucker, J.V.}, year = {2006}, series = {Lecture Notes in Computer Science}, volume = {3988}, pages = {55--64}, publisher = {Springer}, address = {Berlin}, note = {Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006} } @Article{BCGH07, author = {Bournez, Olivier and Campagnolo, Manuel L. and Gra{\c{c}}a, Daniel and S. Hainry, Emmanuel}, title = {Polynomial differential equations compute all real computable functions on computable compact intervals}, journal = {Journal of Complexity}, year = {2007}, volume = {23}, number = {3}, pages = {317--335} } @InProceedings{BCJMR81, author = {Bridges, Douglas and Calder, Allan and Julian, William and Mines, Ray and Richman, Fred}, title = {Locating metric complements in {R}$^n$}, booktitle = {Constructive Mathematics}, editor = {Richman, F.}, year = {1981}, series = {Lecture Notes in Mathematics}, volume = {873}, pages = {241--249}, note = {Proc. New Mexico State Univ. Conf., Aug. 11--15, 1980, Las Cruces, NM} } @Article{BCJMR81a, author = {Bridges, Douglas and Calder, Allan and Julian, William and Mines, Ray and Richman, Fred}, title = {Bounded linear mappings of finite rank}, journal = {Journal of Functional Analysis}, year = {1981}, volume = {43}, number = {2}, pages = {143--148} } @Article{BCJMR82, author = {Bridges, Douglas and Calder, Allan and Julian, William and Mines, Ray and Richman, Fred}, title = {Picard's theorem}, journal = {Trans. Amer. Math. Soc.}, year = {1982}, volume = {269}, number = {2}, pages = {513--520} } @Article{BCPS99, author = {Bridges, D. and Calude, C. and Pavlov, B. and {\c{S}}tef{\u{a}}nescu, D.}, title = {The constructive implicit function theorem and applications in mechanics}, journal = {Chaos, Solitons and Fractals}, year = {1999}, volume = {10}, number = {6}, pages = {927--934} } @InProceedings{BCR07, author = {Brodhead, Paul and Cenzer, Douglas and Remmel, Jeffrey B.}, title = {Random Continuous Functions}, booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis}, editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus}, year = {2007}, series = {Electronic Notes in Theoretical Computer Science}, volume = {167}, publisher = {Elsevier}, address = {Amsterdam}, note = {CCA 2006, Gainesville, Florida, USA, November 1--5, 2006} } @InProceedings{BCRW07, author = {Barmpalias, George and Cenzer, Douglas and Remmel, Jeffrey B. and Weber, Rebecca}, title = {K-Trivial Closed Sets and Continuous Functions}, booktitle = {Computation and Logic in the Real World}, editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea}, year = {2007}, series = {Lecture Notes in Computer Science}, volume = {4497}, pages = {135--145}, publisher = {Springer}, address = {Berlin}, note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007} } @Article{BD00, author = {Bridges, Douglas and Dediu, Lumini{\c{t}}a}, title = {The weak-operator sequential continuity of left multiplication}, journal = {Indagationes Mathematicae}, year = {2000}, volume = {11}, number = {1}, pages = {39--42} } @Article{BD05, author = {Brattka, Vasco and Dillhage, Ruth}, title = {Computability of the Spectrum of Self-Adjoint Operators}, journal = {Journal of Universal Computer Science}, year = {2005}, volume = {11}, number = {12}, pages = {1884--1900} } @Article{BD06a, author = {Bridges, Douglas and Diener, Hannes}, title = {A constructive treatment of {U}rysohn's {L}emma in an apartness space}, journal = {Mathematical Logic Quarterly}, year = {2006}, volume = {52}, number = {5}, pages = {464--469} } @InProceedings{BD07, author = {Brattka, Vasco and Dillhage, Ruth}, title = {On Computable Compact Operators on {B}anach Spaces}, booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis}, editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus}, year = {2007}, series = {Electronic Notes in Theoretical Computer Science}, volume = {167}, pages = {365--386}, publisher = {Elsevier}, address = {Amsterdam}, note = {CCA 2006, Gainesville, Florida, USA, November 1--5, 2006} } @Article{BD07a, author = {Brattka, Vasco and Dillhage, Ruth}, title = {On Computable Compact Operators on Computable {B}anach Spaces with Bases}, journal = {Mathematical Logic Quarterly}, year = {2007}, volume = {53}, number = {4--5}, pages = {345--364} } @Article{BD91, author = {Bridges, Douglas and Demuth, Osvald}, title = {On the {L}ebesgue measurability of continuous functions in constructive analysis}, journal = {BAMS}, year = {1991}, volume = {24}, number = {2}, pages = {259--276} } @Article{BD97, author = {Bridges, Douglas and Dediu, Lumini{\c{t}}a}, title = {Paradise lost, or paradise regained?}, journal = {Bulletin of the European Association for Theoretical Computer Science}, year = {1997}, volume = {63}, pages = {141--155} } @Article{BD98, author = {Bridges, D. S. and Dudley Ward, N. F.}, title = {Constructing ultraweakly continuous functionals on ${B}({H})$}, journal = {Proceedings of the American Mathematical Society}, year = {1998}, volume = {126}, number = {11}, pages = {3347--3353} } @Article{BD99, author = {Bridges, Douglas and Dediu, Lumini{\c{t}}a}, title = {Weak continuity properties in constructive analysis}, journal = {Logic Journal of the IGPL. Interest Group in Pure and Applied Logics}, year = {1999}, volume = {7}, number = {3}, pages = {277--281} } @Article{BD99a, author = {Bridges, Douglas and Dediu, Lumini{\c{t}}a}, title = {Weak-operator continuity and the existence of adjoints}, journal = {Mathematical Logic Quarterly}, year = {1999}, volume = {45}, number = {2}, pages = {203--206} } @Article{BDI03, author = {Bridges, Douglas and van Dalen, Dirk and Ishihara, Hajime}, title = {Ishihara's proof technique in constructive analysis}, journal = {Indagationes Mathematicae}, year = {2003}, volume = {14}, number = {2}, pages = {163--168} } @InProceedings{BES02, author = {Bauer, Andrej and Escard{\'{o}}, Mart{\'{\i}}n H{\"{o}}tzel and Simpson, Alex}, title = {Comparing Functional Paradigms for Exact Real-Number Computation}, booktitle = {Automata, Languages and Programming}, editor = {Widmayer, Peter and Triguero, Francisco and Morales, Rafael and Hennessy, Matthew and Eidenbenz, Stephan and Conejo, Ricardo}, year = {2002}, series = {Lecture Notes in Computer Science}, volume = {2380}, pages = {488--500}, publisher = {Springer}, address = {Berlin}, note = {29th International Colloquium, ICALP, M{\'{a}}laga, Spain, July 8--13, 2002} } @Article{BF02, author = {Becher, Ver{\'{o}}nica and Figueira, Santiago}, title = {An example of a computable absolutely normal number}, journal = {Theoretical Computer Science}, year = {2002}, volume = {270}, pages = {947--958} } @Proceedings{BFM07, title = {Real Numbers}, editor = {Brattka, Vasco and Frougny, Christiane and M{\"u}ller, Norbert}, year = {2007}, series = {Theoretical Informatics and Applications}, volume = {41}, number = {1}, publisher = {EDP Sciences}, address = {Les Ulis}, note = {Selected Papers of the 6th conference on Real Numbers and Computers, Dagstuhl, Germany, November 15-17, 2004} } @Article{BFP07, author = {Becher, Ver{\'{o}}nica and Figueira, Santiago and Picchi, Rafael}, title = {{T}uring’s unpublished algorithm for normal numbers}, journal = {Theoretical Computer Science}, year = {2007}, volume = {377}, number = {1--3}, pages = {126--138} } @Article{BG04, author = {Becher, Ver{\'{o}}nica and Grigorieff, Serge}, title = {Recursion and topology on $2^{\leq\omega}$ for possibly infinite computations}, journal = {Theoretical Computer Science}, year = {2004}, volume = {322}, number = {1}, pages = {85--136} } @InProceedings{BG07, author = {Brattka, Vasco and Gherardi, Guido}, title = {Borel Complexity of Topological Operations on Computable Metric Spaces}, booktitle = {Computation and Logic in the Real World}, editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea}, year = {2007}, series = {Lecture Notes in Computer Science}, volume = {4497}, pages = {83--97}, publisher = {Springer}, address = {Berlin}, note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007} } @Article{BGI04, author = {Bonanno, Claudio and Galatolo, Stefano and Isola, Stefano}, title = {Recurrence and algorithmic information}, journal = {Nonlinearity}, year = {2004}, volume = {17}, number = {3}, pages = {1057--1074} } @Article{BH00a, author = {Bridges, Douglas and Havea, Robin}, title = {A constructive analysis of a proof that the numerical range is convex}, journal = {London Math. Soc. Journal of Mathematics and Computation}, year = {2000}, volume = {3}, pages = {191--206} } @Article{BH01, author = {Bridges, Douglas and Havea, Robin}, title = {A constructive version of the spectral mapping theorem}, journal = {Mathematical Logic Quarterly}, year = {2001}, volume = {47}, number = {3}, pages = {299--304} } @Article{BH02, author = {Brattka, Vasco and Hertling, Peter}, title = {Topological properties of real number representations}, journal = {Theoretical Computer Science}, year = {2002}, volume = {284}, number = {2}, pages = {241--257} } @Article{BH05, author = {Bournez, Olivier and Hainry, Emmanuel}, title = {Elementarily computable functions over the real numbers and $R$-sub-recursive functions}, journal = {Theoretical Computer Science}, year = {2005}, volume = {348}, pages = {130--147} } @Article{BH06, author = {Bournez, Olivier and Hainry, Emmanuel}, title = {Recursive Analysis Characterized as a Class of Real Recursive Functions}, journal = {Fundamenta Mathematicae}, year = {2006}, volume = {74}, number = {4}, pages = {409--433} } @Article{BH07, author = {Bridges, Douglas S. and Havea, Robin}, title = {Powers of a {H}ermitian element}, journal = {New Zealand J. Math.}, year = {2007}, volume = {36}, pages = {1--10} } @TechReport{BH94, author = {Brattka, Vasco and Hertling, Peter}, title = {Continuity and computability of relations}, year = {1994}, month = {September}, number = {164}, type = {Informatik Berichte}, institution = {FernUniversit\"at Hagen}, address = {Hagen} } @Article{BH98, author = {Brattka, Vasco and Hertling, Peter}, title = {Feasible real random access machines}, journal = {Journal of Complexity}, year = {1998}, volume = {14}, number = {4}, pages = {490--526} } @Proceedings{BHKT06, title = {Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Hertling, Peter and Ko, Ker-I and Tsuiki, Hideki}, year = {2006}, series = {Journal of Complexity}, volume = {522}, number = {6}, publisher = {Elsevier}, address = {Amsterdam}, note = {Selected Papers of the International Conference CCA 2005, held in Kyoto, Japan, August 25--29, 2005} } @Proceedings{BHKZ04, title = {Special Issue Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Hertling, Peter and Ko, Ker-I and Zhong, Ning}, year = {2004}, series = {Mathematical Logic Quarterly}, volume = {50}, number = {4,5}, publisher = {Wiley-VCH}, address = {Weinheim}, note = {Selected Papers of the International Conference CCA 2003, held in Cincinnati, Ohio, August 28--30, 2003} } @Article{BHS06, author = {Bridges, Douglas and Havea, Robin and Schuster, Peter}, title = {Ideals in constructive {B}anach algebra theory}, journal = {Journal of Complexity}, year = {2006}, volume = {22}, number = {6}, pages = {729--737} } @Article{BHS06a, author = {Bridges, Douglas and Havea, Robin and Schuster, Peter}, title = {Constructive {B}anach algebra theory and the {N}ullstellensatz}, journal = {Publ. Math. Debrecen}, year = {2006}, volume = {69}, number = {1,2}, pages = {171--184} } @InCollection{BHW08, author = {Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus}, title = {A Tutorial on Computable Analysis}, booktitle = {New Computational Paradigms: Changing Conceptions of What is Computable}, editor = {Cooper, S. Barry and L\"owe, Benedikt and Sorbi, Andrea}, year = {2008}, pages = {425--491}, publisher = {Springer}, address = {New York} } @Proceedings{BHYZ02, title = {Selected Papers of the Dagstuhl Seminar on Computability and Complexity in Analysis 2001}, editor = {Brattka, Vasco and Hertling, Peter and Yasugi, Mariko and Zhong, Ning}, year = {2002}, series = {Mathematical Logic Quarterly}, volume = {48 (Suppl. 1)}, publisher = {Wiley-VCH}, address = {Weinheim} } @Article{BI01, author = {Bridges, Douglas and Ishihara, Hajime}, title = {Constructive closed range and open mapping theorems}, journal = {Indagationes Mathematicae}, year = {2001}, volume = {11}, number = {4}, pages = {509--516} } @InProceedings{BI01a, author = {Bridges, Douglas and Ishihara, Hajime}, title = {Constructive unbounded operators}, booktitle = {Reuniting the antipodes---constructive and nonstandard views of the continuum (Venice, 1999)}, editor = {Schuster, Peter and Berger, Ulrich and Osswald, Horst}, year = {2001}, series = {Synthese Library}, volume = {306}, pages = {25--37}, publisher = {Kluwer Acad. Publ.}, address = {Dordrecht} } @Article{BI05, author = {Berger, Josef and Ishihara, Hajime}, title = {Brouwer's fan theorem and unique existence in constructive analysis}, journal = {Mathematical Logic Quarterly}, year = {2005}, volume = {51}, number = {4}, pages = {360--364} } @Article{BI90, author = {Bridges, Douglas and Ishihara, Hajime}, title = {Linear mappings are fairly well-behaved}, journal = {Archiv der Mathematik. Archives of Mathematics. Archives Math\'ematiques}, year = {1990}, volume = {54}, number = {6}, pages = {558--562} } @Article{BI92, author = {Bridges, Douglas and Ishihara, Hajime}, title = {Locating the range of an operator on a {H}ilbert space}, journal = {The Bulletin of the London Mathematical Society}, year = {1992}, volume = {24}, number = {6}, pages = {599--605} } @Article{BI94, author = {Bridges, Douglas S. and Ishihara, Hajime}, title = {Complements of intersections in constructive mathematics}, journal = {Mathematical Logic Quarterly}, year = {1994}, volume = {40}, number = {1}, pages = {35--43} } @Article{BI94a, author = {Bridges, Douglas and Ishihara, Hajime}, title = {Absolute continuity and the uniqueness of the constructive functional calculus}, journal = {Mathematical Logic Quarterly}, year = {1994}, volume = {40}, number = {4}, pages = {519--527} } @Article{BI94b, author = {Bridges, Douglas S. and Ishihara, Hajime}, title = {Erratum: ``{C}omplements of intersections in constructive mathematics''}, journal = {Mathematical Logic Quarterly}, year = {1994}, volume = {40}, number = {4}, pages = {570} } @Article{BI96, author = {Bridges, Douglas and Ishihara, Hajime}, title = {Spectra of selfadjoint operators in constructive analysis}, journal = {Indagationes Mathematicae}, year = {1996}, volume = {7}, number = {1}, pages = {11--35} } @Article{BI98, author = {Bridges, Douglas and Ishihara, Hajime}, title = {A definite constructive open mapping theorem?}, journal = {Mathematical Logic Quarterly}, year = {1998}, volume = {44}, number = {4}, pages = {545--552} } @Article{BIMRSV07, author = {Bridges, Douglas and Ishihara, Hajime and Mines, Ray and Richman, Fred and Schuster, Peter M. and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {Almost locatedness in uniform spaces}, journal = {Czechoslovak Math. J.}, year = {2007}, volume = {57}, number = {1}, pages = {1--12} } @InProceedings{BIS02, author = {Bridges, Douglas and Ishihara, Hajime and Schuster, Peter}, title = {Compactness and continuity, constructively revisited}, booktitle = {Computer science logic}, editor = {Bradfield, Julian}, year = {2002}, series = {Lecture Notes in Computer Science}, volume = {2471}, pages = {89--102}, publisher = {Springer} } @Article{BIS03, author = {Bridges, Douglas and Ishihara, Hajime and Spitters, Bas}, title = {Locating the range of an operator with an adjoint}, journal = {Indagationes Mathematicae}, year = {2003}, volume = {13}, number = {4}, pages = {433--440} } @Article{BIS99, author = {Bridges, Douglas and Ishihara, Hajime and Schuster, Peter}, title = {Sequential Compactness in Constructive Analysis}, journal = {\"{O}sterr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II.}, year = {1999}, volume = {208}, pages = {159--163} } @Proceedings{BISZ08, title = {Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Ishihara, Hajime and Schr{\"o}der, Matthias and Zhong, Ning}, year = {2008}, series = {Journal of Universal Computer Science}, volume = {14}, number = {6}, publisher = {Graz University of Technology}, address = {Graz}, note = {Selected Papers of the Fourth International Conference on Computability and Complexity in Analysis, June 16-18, 2007, Siena, Italy} } @Article{BIV04, author = {Bridges, Douglas and Ishihara, Hajime and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {Computing infima on convex sets, with applications in {H}ilbert spaces}, journal = {Proceedings of the American Mathematical Society}, year = {2004}, volume = {132}, number = {9}, pages = {2723--2732} } @Article{BIV06, author = {Bridges, Douglas and Ishihara, Hajime and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {A new constructive version of {B}aire's Theorem}, journal = {Hokkaido Math. Journal}, year = {2006}, volume = {35}, number = {1}, pages = {107--118} } @InProceedings{BJL01, author = {Breutzmann, Josef M. and Juedes, David W. and Lutz, Jack H.}, title = {Baire Category and Nowhere Differentiability for Feasible Real Functions}, booktitle = {Algorithms and Computation}, editor = {Eades, Peter and Takaoka, Tadao}, year = {2001}, series = {Lecture Notes in Computer Science}, volume = {2223}, pages = {219--230}, publisher = {Springer}, address = {Berlin}, note = {12th International Symposium, ISAAC 2001, Christchurch, New Zealand, December 19-21, 2001} } @Article{BJL04, author = {Breutzmann, Josef M. and Juedes, David W. and Lutz, Jack H.}, title = {Baire category and nowhere differentiability for feasible real functions}, journal = {Mathematical Logic Quarterly}, year = {2004}, volume = {50}, number = {4,5}, pages = {460--472} } @Article{BJM89, author = {Bridges, Douglas and Julian, William and Mines, Ray}, title = {A constructive treatment of open and unopen mapping theorems}, journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik}, year = {1989}, volume = {35}, number = {1}, pages = {29--43} } @Article{BJRM92, author = {Bridges, D.S. and Julian, W.H. and Richman, F. and Mines, R.}, title = {Extensions and fixed points of contractive maps in {R}$^n$}, journal = {J. Math. Anal. Appl.}, year = {1992}, volume = {165}, pages = {438--456} } @InProceedings{BK08, author = {Bauer, Andrej and Kavkler, Iztok}, title = {Implementing real numbers with {RZ}}, booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)}, editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning}, year = {2008}, series = {Electronic Notes in Theoretical Computer Science}, volume = {202}, pages = {365--384}, publisher = {Elsevier}, note = {CCA 2007, Siena, Italy, June 16--18, 2007} } @InCollection{BK98, author = {Brattka, Vasco and Kalantari, Iraj}, title = {A Bibliography of Recursive Analysis and Recursive Topology}, booktitle = {Handbook of Recursive Mathematics}, editor = {Ershov, Yu. L. and Goncharov, S.S. and Nerode, A. and Remmel, J.B.}, year = {1998}, series = {Studies in Logic and the Foundations of Mathematics}, volume = {138}, pages = {583--620}, publisher = {Elsevier}, address = {Amsterdam}, note = {Volume 1, Recursive Model Theory} } @InProceedings{BL00, author = {Burrows, Ashley and Lester, David}, title = {Exact Arithmetic and the {K}orteweg-de {V}ries Equation}, booktitle = {Computability and Complexity in Analysis}, editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus}, year = {2000}, month = {September}, series = {Informatik Berichte}, volume = {272}, pages = {23--41}, publisher = {FernUniversit\"at Hagen}, note = {CCA 2000 Workshop, Swansea, Wales, September 17--19, 2000} } @Article{BM00, author = {Bridges, Douglas and Mahalanobis, Ayan}, title = {Sequential continuity of functions in constructive analysis}, journal = {Mathematical Logic Quarterly}, year = {2000}, volume = {46}, number = {1}, pages = {139--143} } @Article{BM01, author = {Bridges, Douglas and Mahalanobis, Ayan}, title = {Increasing, nondecreasing, and virtually continuous functions}, journal = {Journal of Automata, Languages and Combinatorics}, year = {2001}, volume = {6}, number = {2}, pages = {139--143} } @Article{BM01a, author = {Bridges, Douglas and Mahalanobis, Ayan}, title = {Bounded variation implies regulated: a constructive proof}, journal = {The Journal of Symbolic Logic}, year = {2001}, volume = {66}, number = {4}, pages = {1695--1700} } @InProceedings{BM07, author = {Bienvenu, Laurent and Merkle, Wolfgang}, title = {Effective randomness for computable probability measures}, booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis}, editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus}, year = {2007}, series = {Electronic Notes in Theoretical Computer Science}, volume = {167}, pages = {117--130}, publisher = {Elsevier}, address = {Amsterdam}, note = {CCA 2006, Gainesville, Florida, USA, November 1--5, 2006} } @InProceedings{BM07a, author = {Barmpalias, George and Montalb{\'a}n, Antonio}, title = {A cappable almost everywhere dominating computably enumerable degree}, booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis}, editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus}, year = {2007}, series = {Electronic Notes in Theoretical Computer Science}, volume = {167}, pages = {17--31}, publisher = {Elsevier}, address = {Amsterdam}, note = {CCA 2006, Gainesville, Florida, USA, November 1--5, 2006} } @Article{BM37, author = {Banach, Stefan and Mazur, Stanis{\l}aw}, title = {Sur les fonctions calculables}, journal = {Ann. Soc. Pol. de Math.}, year = {1937}, volume = {16}, pages = {223} } @Article{BM84, author = {Bridges, D.S. and Mines, R.}, title = {What is constructive mathematics?}, journal = {The Mathematical Intelligencer}, year = {1984}, volume = {6}, number = {4}, pages = {32--38} } @Article{BM98, author = {Bridges, Douglas and Mines, Ray}, title = {Sequentially continuous linear mappings in constructive analysis}, journal = {The Journal of Symbolic Logic}, year = {1998}, volume = {63}, number = {2}, pages = {579--583} } @Article{BMRS04, author = {Bridges, Douglas and Mines, Ray and Richman, Fred and Schuster, Peter}, title = {The polydisk {N}ullstellensatz}, journal = {Proceedings of the American Mathematical Society}, year = {2004}, volume = {132}, number = {7}, pages = {2133--2140} } @Article{BP03, author = {Brattka, Vasco and Presser, Gero}, title = {Computability on subsets of metric spaces}, journal = {Theoretical Computer Science}, year = {2003}, volume = {305}, pages = {43--76} } @Article{BP03a, author = {Bridges, Douglas and Popa, Gabriela}, title = {Exact, continuous boundary crossings out of convex sets in $R^N$}, journal = {The Quarterly Journal of Mathematics}, year = {2003}, volume = {54}, number = {4}, pages = {391--398} } @Article{BR87, author = {Brady, S.S. and Remmel, J.B.}, title = {The undecidability of the lattice of r.e. closed subsets of an effective topological space}, journal = {Annals of Pure and Applied Logic}, year = {1987}, volume = {35}, pages = {193--203} } @Book{BR87a, author = {Bridges, Douglas and Richman, Fred}, title = {Varieties of Constructive Mathematics}, year = {1987}, series = {London Mathematical Society Lecture Note Series}, volume = {97}, publisher = {Cambridge University Press}, address = {Cambridge} } @Article{BR91, author = {Bridges, Douglas S. and Richman, Fred}, title = {A recursive counterexample to {D}ebreu's theorem on the existence of a utility function}, journal = {Mathematical Social Sciences}, year = {1991}, volume = {21}, number = {2}, pages = {179--182} } @Article{BR99, author = {Bridges, Douglas and Reeves, Steve}, title = {Constructive mathematics in theory and programming practice}, journal = {Philosophia Mathematica. Philosophy of Mathematics, its Learning, and its Application. Series III}, year = {1999}, volume = {7}, number = {1}, pages = {65--104}, note = {Mathematical proof} } @Article{BRJM92, author = {Bridges, D. S. and Richman, F. and Julian, W. H. and Mines, R.}, title = {Extensions and fixed points of contractive maps in ${\bf{R}}\sp n$}, journal = {Journal of Mathematical Analysis and Applications}, year = {1992}, volume = {165}, number = {2}, pages = {438--456} } @Article{BRS00, author = {Bridges, Douglas and Richman, Fred and Schuster, Peter}, title = {Linear independence without choice}, journal = {Annals of Pure and Applied Logic}, year = {2000}, volume = {101}, number = {1}, pages = {95--102} } @Article{BRS00a, author = {Bridges, Douglas and Richman, Fred and Schuster, Peter}, title = {A weak countable choice principle}, journal = {Proceedings of the American Mathematical Society}, year = {2000}, volume = {128}, number = {9}, pages = {2749--2752} } @Article{BRS00b, author = {Bridges, Douglas and Richman, Fred and Schuster, Peter}, title = {Adjoints, absolute values, and polar decompositions}, journal = {J. Operator Theory}, year = {2000}, volume = {44}, number = {2}, pages = {243--254} } @Article{BRY96, author = {Bridges, Douglas and Richman, Fred and Yuchuan, Wang}, title = {Sets, complements and boundaries}, journal = {Indagationes Mathematicae}, year = {1996}, volume = {7}, number = {4}, pages = {425--445} } @Article{BS00, author = {Bridges, Douglas and Svozil, Karl}, title = {Constructive mathematics and quantum physics}, journal = {J. Theor. Physics}, year = {2000}, volume = {39}, pages = {501--513} } @InProceedings{BS03, author = {Bauer, Andrej and Simpson, Alex}, title = {Locally non-compact spaces and continuity principles}, booktitle = {Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning}, year = {2003}, month = {August}, series = {Informatik Berichte}, volume = {302}, pages = {103--116}, publisher = {FernUniversit\"at in Hagen}, note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003} } @Article{BS04, author = {Bauer, Andrej and Simpson, Alex}, title = {Two constructive embedding-extension theorems with applications to continuity principles and to {B}anach-{M}azur computability}, journal = {Mathematical Logic Quarterly}, year = {2004}, volume = {50}, number = {4,5}, pages = {351--369} } @InProceedings{BS05, author = {Brattka, Vasco and Schr{\"{o}}der, Matthias}, title = {Computing with Sequences, Weak Topologies and the Axiom of Choice}, booktitle = {Computer science logic}, editor = {Ong, Luke}, year = {2005}, series = {Lecture Notes in Computer Science}, volume = {3634}, pages = {462--476}, publisher = {Springer} } @Article{BS05a, author = {Badaev, Serikzhan and Spreen, Dieter}, title = {A note on partial numberings}, journal = {Mathematical Logic Quarterly}, year = {2005}, volume = {51}, number = {2}, pages = {129--136} } @Article{BS06, author = {Bridges, Douglas and Schuster, Peter}, title = {A simple constructive proof of {K}ronecker's density theorem}, journal = {Elemente der Mathematik}, year = {2006}, volume = {61}, pages = {152--154} } @InProceedings{BS07, author = {Bauer, Andrej and Stone, Christopher A.}, title = {{RZ}: {A} Tool for Bringing Constructive and Computable Mathematics Closer to Programming Practice}, booktitle = {Computation and Logic in the Real World}, editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea}, year = {2007}, series = {Lecture Notes in Computer Science}, volume = {4497}, pages = {28--42}, publisher = {Springer}, address = {Berlin}, note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007} } @Article{BS07a, author = {Becher, Ver{\'{o}}nica and Grigorieff, Serge}, title = {Random reals {\'a} la {C}haitin with or without prefix-freeness}, journal = {Theoretical Computer Science}, year = {2007}, volume = {385}, pages = {193--201} } @Article{BST02, author = {Blanck, Jens and Stoltenberg-Hansen, Viggo and Tucker, John V.}, title = {Domain representations of partial functions, with applications to spatial objects and constructive volume geometry}, journal = {Theoretical Computer Science}, year = {2002}, volume = {284}, number = {2}, pages = {207--240} } @Article{BSV02, author = {Bridges, Douglas and Schuster, Peter and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {Apartness, Topology, and Uniformity: a Constructive View}, journal = {Mathematical Logic Quarterly}, year = {2002}, volume = {48}, number = {Suppl. 1}, pages = {16--28} } @Proceedings{BSW02, title = {Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus}, year = {2002}, series = {Electronic Notes in Theoretical Computer Science}, volume = {66(1)}, publisher = {Elsevier}, address = {Amsterdam}, note = {5th International Workshop, CCA 2002, M{\'{a}}laga, Spain, July 12--13, 2002} } @Proceedings{BSW05, title = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus}, year = {2005}, series = {Electronic Notes in Theoretical Computer Science}, volume = {120}, publisher = {Elsevier}, address = {Amsterdam}, note = {6th International Workshop, CCA 2004, Wittenberg, Germany, August 16--20, 2004} } @TechReport{BSWZ03, author = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning}, title = {Computability and Complexity in Analysis}, year = {2003}, month = {August}, number = {302}, type = {Informatik Berichte}, institution = {FernUniversit\"at in Hagen}, address = {Hagen}, note = {Proccedings, International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003} } @InProceedings{BT05, author = {Bauer, Andrej and Taylor, Paul}, title = {The {D}edekind reals in abstract {S}tone duality}, booktitle = {Computability and Complexity in Analysis}, editor = {Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus}, year = {2005}, month = {July}, series = {Informatik Berichte}, volume = {326}, pages = {25--64}, publisher = {FernUniversit\"at in Hagen}, note = {Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25--29, 2005} } @Article{BT07, author = {Beggs, Edwin J. and Tucker, John V.}, title = {Can {N}ewtonian systems, bounded in space, time, mass and energy compute all functions?}, journal = {Theoretical Computer Science}, year = {2007}, volume = {371}, pages = {4--19} } @Article{BV00, author = {Bridges, Douglas and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {Constructing extensions of ultraweakly continuous linear functionals}, journal = {J. Functional Analysis}, year = {2000}, volume = {178}, number = {2}, pages = {421--434} } @Article{BV01, author = {Bridges, Douglas and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {Characterising Near Continuity Constructively}, journal = {Mathematical Logic Quarterly}, year = {2001}, volume = {47}, number = {4}, pages = {535--538} } @Article{BV02, author = {Bridges, Douglas and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {Cauchy nets in the constructive theory of apartness spaces}, journal = {Scientiae Mathematicae Japonicae}, year = {2002}, volume = {56}, number = {1}, pages = {123--132} } @Article{BV03, author = {Bridges, Douglas and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {Apartness spaces as a framework for constructive topology}, journal = {Annals of Pure and Applied Logic}, year = {2003}, volume = {119}, number = {1-3}, pages = {61--83} } @Article{BV03a, author = {Bridges, Douglas and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {A proof-technique in uniform space theory}, journal = {The Journal of Symbolic Logic}, year = {2003}, volume = {68}, number = {3}, pages = {795--802} } @Article{BV03b, author = {Bridges, Douglas and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {Separatedness in constructive topology}, journal = {Documenta Mathematica}, year = {2003}, volume = {8}, pages = {567--576} } @Article{BV03c, author = {Bridges, Douglas and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {Cauchy nets in uniform apartness spaces}, journal = {Revue Roumaine de Math\'ematiques Pures et Appliqu\'ees}, year = {2003}, volume = {48}, number = {5-6}, pages = {467--474} } @Article{BV03d, author = {Bridges, Douglas and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {Strong and uniform continuity---the uniform space case}, journal = {LMS Journal of Computation and Mathematics}, year = {2003}, volume = {6}, pages = {326--334} } @Article{BV04a, author = {Bridges, Douglas and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {Corrigendum to: ``{A} proof-technique in uniform space theory''}, journal = {The Journal of Symbolic Logic}, year = {2004}, volume = {69}, number = {1}, pages = {328} } @InProceedings{BV05, author = {Bridges, Douglas and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {A general constructive proof technique}, booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus}, year = {2005}, series = {Electronic Notes in Theoretical Computer Science}, volume = {120}, pages = {31--43}, publisher = {Elsevier}, address = {Amsterdam}, note = {6th International Workshop, CCA 2004, Wittenberg, Germany, August 16--20, 2004} } @InProceedings{BV05a, author = {Bridges, Douglas and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {An extension theorem for ultraweakly continuous linear functionals on $B(X,Y)$}, booktitle = {Computability and Complexity in Analysis}, editor = {Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus}, year = {2005}, month = {July}, series = {Informatik Berichte}, volume = {326}, pages = {77--89}, publisher = {FernUniversit\"at in Hagen}, note = {Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25--29, 2005} } @InProceedings{BV05b, author = {Bridges, Douglas and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {Proximal connectedness}, booktitle = {Computability and Complexity in Analysis}, editor = {Grubba, Tanja and Hertling, Peter and Tsuiki, Hideki and Weihrauch, Klaus}, year = {2005}, month = {July}, series = {Informatik Berichte}, volume = {326}, pages = {91--101}, publisher = {FernUniversit\"at in Hagen}, note = {Proccedings, Second International Conference, CCA 2005, Kyoto, Japan, August 25--29, 2005} } @Book{BV06, author = {Bridges, Douglas and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {Techniques of Constructive Analysis}, year = {2006}, publisher = {Springer}, address = {New York} } @Article{BV06a, author = {Bridges, Douglas and V{\^{\i}}{\c{t}}{\u{a}}, Lumini{\c{t}}a}, title = {Pre-apartness structures on spaces of functions}, journal = {Journal of Complexity}, year = {2006}, volume = {22}, number = {6}, pages = {881--893} } @Article{BV98, author = {Boldi, Paolo and Vigna, Sebastiano}, title = {$\delta$-uniform {BSS} Machines}, journal = {Journal of Complexity}, year = {1998}, volume = {14}, number = {2}, pages = {234--256} } @Article{BV99, author = {Boldi, Paolo and Vigna, Sebastiano}, title = {Equality is a Jump}, journal = {Theoretical Computer Science}, year = {1999}, volume = {219}, pages = {49--64} } @Article{BW02, author = {Bridges, Douglas S. and Ward, Nicholas Dudley}, title = {Kernels of seminorms in constructive analysis}, journal = {Theoretical Computer Science}, year = {2002}, volume = {284}, number = {2}, pages = {259--267} } @Article{BW97, author = {Bridges, Douglas and Wang, Yuchuan}, title = {Constructive aspects of the {D}irichlet problem}, journal = {Journal of Universal Computer Science}, year = {1997}, volume = {3}, number = {11}, pages = {1148--1161 (electronic)}, note = {Proceedings of the First Japan-New Zealand Workshop on Logic in Computer Science (Auckland, 1997)} } @Article{BW97a, author = {Bridges, Douglas and Wang, Yuchuan}, title = {Constructing cutoff functions}, journal = {New Zealand Journal of Mathematics}, year = {1997}, volume = {26}, number = {1}, pages = {25--30} } @Article{BW98a, author = {Bridges, Douglas and Wang, Yuchuan}, title = {Constructive weak solutions of the {D}irichlet problem}, journal = {The Journal of the London Mathematical Society. Second Series}, year = {1998}, volume = {57}, number = {3}, pages = {655--667} } @Article{BW98b, author = {Bridges, Douglas and Wang, Yuchuan}, title = {Constructing best approximations on a {J}ordan curve}, journal = {Journal of Approximation Theory}, year = {1998}, volume = {94}, number = {2}, pages = {222--234} } @Article{BW98c, author = {Bridges, Douglas and Wang, Yuchuan}, title = {Weak solutions of the {D}irichlet problem and the locatedness of ${H}\sp 1\sb 0(\Omega)$}, journal = {New Zealand Journal of Mathematics}, year = {1998}, volume = {27}, number = {1}, pages = {1--5} } @Article{BW99, author = {Brattka, Vasco and Weihrauch, Klaus}, title = {Computability on Subsets of {E}uclidean Space {I}: Closed and Compact Subsets}, journal = {Theoretical Computer Science}, year = {1999}, volume = {219}, pages = {65--93} } @Article{BY06, author = {Brattka, Vasco and Yoshikawa, Atsushi}, title = {Towards computability of elliptic boundary value problems in variational formulation}, journal = {Journal of Complexity}, year = {2006}, volume = {22}, number = {6}, pages = {858--880} } @Article{BY06a, author = {Braverman, Mark and Yampolsky, M.}, title = {Non-computable {J}ulia sets}, journal = {Journal of the American Mathematical Society}, year = {2006}, volume = {19}, number = {3}, pages = {551--578} } @InProceedings{BZ02, author = {Brattka, Vasco and Ziegler, Martin}, title = {Computability of linear equations}, booktitle = {Foundations of Information Technology in the Era of Network and Mobile Computing}, editor = {Baeza-Yates, Ricardo and Montanari, Ugo and Santoro, Nicola}, year = {2002}, series = {IFIP International Federation for Information Processing}, volume = {223}, pages = {95--106}, publisher = {Kluwer Academic Publishers}, address = {Dordrecht}, note = {2nd IFIP International Conference on Theoretical Computer Science, Montr{\'e}al, Canada, August 25--30, 2002} } @Article{Bae83, author = {Baez, J.C.}, title = {Recursivity in quantum mechanics}, journal = {Trans. Amer. Math. Soc.}, year = {1983}, volume = {280}, pages = {339--350} } @Article{Bai85, author = {Baigger, G.}, title = {Die {N}ichtkonstruktivit{\"a}t des {B}rouwerschen {F}ixpunktsatzes}, journal = {Arch. Math. Logik Grundlag.}, year = {1985}, volume = {25}, pages = {183--188} } @Article{Bai99, author = {Baire, R.}, title = {Sur les fonctions des variables reeles}, journal = {Annali di matematica pura ed applicata}, year = {1899}, series = {3}, volume = {3}, pages = {1--123} } @InProceedings{Bar02, author = {Barmpalias, George}, title = {On $0'$-computable Reals}, booktitle = {{CCA} 2002 Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus}, year = {2002}, series = {Electronic Notes in Theoretical Computer Science}, volume = {66}, publisher = {Elsevier}, address = {Amsterdam}, note = {5th International Workshop, CCA 2002, M{\'{a}}laga, Spain, July 12--13, 2002} } @Article{Bar03, author = {Barmpalias, George}, title = {A transfinite hierarchy of reals}, journal = {Mathematical Logic Quarterly}, year = {2003}, volume = {49}, number = {2}, pages = {163--172} } @Article{Bar03a, author = {Barmpalias, George}, title = {The approximation structure of a computably approximable real}, journal = {The Journal of Symbolic Logic}, year = {2003}, volume = {68}, number = {3}, pages = {885--922} } @Article{Bar04, author = {Barmpalias, George}, title = {Approximation representations for reals and their wtt-degrees}, journal = {Mathematical Logic Quarterly}, year = {2004}, volume = {50}, number = {4,5}, pages = {370--380} } @PhdThesis{Bar04a, author = {Barmpalias, Georgios}, title = {Computability and Applications to Analysis}, year = {2004}, school = {University of Leeds, School of Mathematics}, address = {Leeds} } @Article{Bar04b, author = {Barmpalias, George}, title = {Approximation representations for $\Delta_2$ reals}, journal = {Archive for Mathematical Logic}, year = {2004}, volume = {43}, number = {8}, pages = {947--964} } @Article{Bar05, author = {Baroni, Marian Alexandru}, title = {Constructive Suprema}, journal = {Journal of Universal Computer Science}, year = {2005}, volume = {11}, number = {12}, pages = {1865--1877} } @Article{Bar06, author = {Barmpalias, George}, title = {Random non-cupping revisited}, journal = {Journal of Complexity}, year = {2006}, volume = {22}, number = {6}, pages = {850--857} } @InProceedings{Bat08, author = {Batra, Prashant}, title = {Newton's method and the Computational Complexity of the Fundamental Theorem of Algebra}, booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)}, editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning}, year = {2008}, series = {Electronic Notes in Theoretical Computer Science}, volume = {202}, pages = {201--218}, publisher = {Elsevier}, note = {CCA 2007, Siena, Italy, June 16--18, 2007} } @PhdThesis{Bau00, author = {Bauer, Andrej}, title = {The Realizability Approach to Computable Analysis and Topology}, year = {2000}, school = {School of Computer Science, Carnegie Mellon University}, address = {Pittsburgh} } @InProceedings{Bau01, author = {Bauer, Andrej}, title = {A Relationship between Equilogical Spaces and Type Two Effectivity}, booktitle = {Seventeenth Conference on the Mathematical Foundations of Programming Semantics}, editor = {Brooks, Stephen and Mislove, Michael}, year = {2001}, series = {Electronic Notes in Theoretical Computer Science}, volume = {45}, publisher = {Elsevier}, address = {Amsterdam}, note = {MFPS 2001, Aarhus, Denmark May 23--26, 2001} } @Article{Bau02, author = {Bauer, Andrej}, title = {A Relationship between Equilogical Spaces and Type Two Effectivity}, journal = {Mathematical Logic Quarterly}, year = {2002}, volume = {48}, number = {Suppl. 1}, pages = {1--15} } @InCollection{Bee05, author = {Beeson, Michael}, title = {Constructivity, Computability, and the Continuum}, booktitle = {Essays on the Foundations of Mathematics and Logic}, editor = {Sica, Giandomenico}, year = {2005}, series = {Advanced Studies in Mathematics and Logic}, volume = {2}, pages = {9--37}, publisher = {Polimetrica}, address = {Milano} } @InProceedings{Bee80, author = {Beeson, M.J.}, title = {Problematic principles in constructive mathematics}, booktitle = {Logic Colloquium '80}, year = {1980}, series = {Studies in Logic and the Foundations of Mathematics}, volume = {108}, pages = {11--55}, publisher = {North-Holland}, address = {Amsterdam} } @Book{Bee85, author = {Beeson, M.J.}, title = {Foundations of {C}onstructive {M}athematics}, year = {1985}, series = {Ergeb. Math. Grenzgeb.}, publisher = {Springer}, address = {Berlin} } @Article{Ber05, author = {Berger, Josef}, title = {Exact calculation of inverse functions}, journal = {Mathematical Logic Quarterly}, year = {2005}, volume = {51}, number = {2}, pages = {201--205} } @Article{Ber05a, author = {Berger, Josef}, title = {Constructive Equivalents of the Uniform Continuity Theorem}, journal = {Journal of Universal Computer Science}, year = {2005}, volume = {11}, number = {12}, pages = {1878--1883} } @InProceedings{Ber06, author = {Berger, Josef}, title = {The Logical Strength of the Uniform Continuity Theorem}, booktitle = {Logical Approaches to Computational Barriers}, editor = {Beckmann, A. and Berger, U. and L{\"o}we, B. and Tucker, J.V.}, year = {2006}, series = {Lecture Notes in Computer Science}, volume = {3988}, pages = {35--39}, publisher = {Springer}, address = {Berlin}, note = {Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006} } @Article{Ber07, author = {Bertot, Yves}, title = {Affine functions and series with co-inductive real numbers}, journal = {Mathematical Structures in Computer Science}, year = {2007}, volume = {17}, pages = {37--63} } @InProceedings{Bis66, author = {Bishop, Errett}, title = {Constructive {M}ethods in the {T}heory of {B}anach {A}lgebras}, booktitle = {Function Algebras}, editor = {Birtel, F.T.}, year = {1966}, pages = {343--345}, publisher = {Scott-Foresman}, address = {Chicago}, note = {Proc. Internat. Sympos. on Function Algebras, Tulane Univ., 1965} } @Book{Bis67, author = {Bishop, Errett}, title = {Foundations of Constructive Analysis}, year = {1967}, publisher = {McGraw-Hill}, address = {New York} } @Article{Bis67a, author = {Bishop, Errett}, title = {A constructive ergodic theorem}, journal = {J. Math. Mech.}, year = {1967/1968}, volume = {17}, pages = {631--639} } @Article{Bis68, author = {Bishop, Errett}, title = {The constructivization of abstract mathematical analysis}, journal = {Izdat. Mir}, year = {1968}, pages = {308--313}, note = {Proc. Internat. Congr. Math., Moscow, 1968} } @Article{Bla00, author = {Blanck, Jens}, title = {Domain representations of topological spaces}, journal = {Theoretical Computer Science}, year = {2000}, volume = {247}, pages = {229--255} } @InProceedings{Bla01, author = {Blanck, Jens}, title = {Effectivity of Regular Spaces}, booktitle = {Computability and Complexity in Analysis}, editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter}, year = {2001}, series = {Lecture Notes in Computer Science}, volume = {2064}, pages = {1--15}, publisher = {Springer}, address = {Berlin}, note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000} } @InProceedings{Bla01a, author = {Blanck, Jens}, title = {Exact Real Arithmetic Systems: Results of Competition}, booktitle = {Computability and Complexity in Analysis}, editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter}, year = {2001}, series = {Lecture Notes in Computer Science}, volume = {2064}, pages = {389--393}, publisher = {Springer}, address = {Berlin}, note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000} } @Article{Bla02, author = {Bl{\"a}ser, Markus}, title = {Uniform computational complexity of the derivatives of {$C^\infty$}-functions}, journal = {Theoretical Computer Science}, year = {2002}, volume = {284}, number = {2}, pages = {199--206} } @Article{Bla05, author = {Blanck, Jens}, title = {Efficient exact computation of iterated maps}, journal = {The Journal of Logic and Algebraic Programming}, year = {2005}, volume = {64}, pages = {41--59} } @Article{Bla97, author = {Blanck, Jens}, title = {Domain representability of metric spaces}, journal = {Annals of Pure and Applied Logic}, year = {1997}, volume = {83}, pages = {225--247} } @PhdThesis{Bla97a, author = {Blanck, Jens}, title = {Computability on topological spaces by effective domain representations}, year = {1997}, school = {Uppsala University, Department of Mathematics}, address = {Uppsala, Sweden} } @Article{Bla99, author = {Blanck, Jens}, title = {Effective domain representations of {$H(X)$}, the space of compact subsets}, journal = {Theoretical Computer Science}, year = {1999}, volume = {219}, pages = {19--48} } @Article{Boe05, author = {Boehm, Hans-J.}, title = {The constructive reals as a {J}ava library}, journal = {The Journal of Logic and Algebraic Programming}, year = {2005}, volume = {64}, pages = {3--11} } @InProceedings{Bos07, author = {Bosserhoff, Volker}, title = {Computability of solutions of operator equations}, booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis}, editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus}, year = {2007}, series = {Electronic Notes in Theoretical Computer Science}, volume = {167}, pages = {179--202}, publisher = {Elsevier}, address = {Amsterdam}, note = {CCA 2006, Gainesville, Florida, USA, November 1--5, 2006} } @Article{Bos07a, author = {Bosserhoff, Volker}, title = {Computability of solutions of operator equations}, journal = {Mathematical Logic Quarterly}, year = {2007}, volume = {53}, number = {4--5}, pages = {326--344} } @InProceedings{Bos08, author = {Bosserhoff, Volker}, title = {Notions of Probabilistic Computability on Represented Spaces}, booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)}, editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning}, year = {2008}, series = {Electronic Notes in Theoretical Computer Science}, volume = {202}, pages = {137--170}, publisher = {Elsevier}, note = {CCA 2007, Siena, Italy, June 16--18, 2007} } @Article{Bos08a, author = {Bosserhoff, Volker}, title = {The Bit-Complexity of Finding Nearly Optimal Quadrature Rules for Weighted Integration}, journal = {Journal of Universal Computer Science}, year = {2008}, volume = {14}, number = {6}, pages = {938--955} } @Article{Bos08b, author = {Bosserhoff, Volker}, title = {Notions of Probabilistic Computability on Represented Spaces}, journal = {Journal of Universal Computer Science}, year = {2008}, volume = {14}, number = {6}, pages = {956--995} } @InProceedings{Bra00a, author = {Brattka, Vasco}, title = {Realistic models of computability on the real numbers}, booktitle = {Relevance and Feasibility of Mathematical Analysis on the Computer}, editor = {Yoshikawa, Atsushi}, year = {2000}, series = {S\={u}rikaisekikenky\={u}sho K\={o}ky\={u}roku}, volume = {1169}, pages = {62--75}, publisher = {Research Institute for Mathematical Sciences}, address = {Kyoto} } @InProceedings{Bra01a, author = {Brattka, Vasco}, title = {Computable versions of {B}aire's category theorem}, booktitle = {Mathematical Foundations of Computer Science 2001}, editor = {Sgall, Ji{\v{r}}{\'{\i}} and Pultr, Ale{\v{s}} and Kolman, Petr}, year = {2001}, series = {Lecture Notes in Computer Science}, volume = {2136}, pages = {224--235}, publisher = {Springer}, address = {Berlin}, note = {26th International Symposium, MFCS 2001, Mari{\'{a}}nsk{\'{e}} L{\'{a}}zn{\v{e}}, Czech Republic, August 27-31, 2001} } @TechReport{Bra01b, author = {Brattka, Vasco}, title = {Computability of {B}anach Space Principles}, year = {2001}, month = {June}, number = {286}, type = {Informatik Berichte}, institution = {FernUniversit\"at Hagen, Fachbereich Informatik}, address = {Hagen} } @InProceedings{Bra02b, author = {Brattka, Vasco}, title = {Random Numbers and an Incomplete Immune Recursive Set}, booktitle = {Automata, Languages and Programming}, editor = {Widmayer, Peter and Triguero, Francisco and Morales, Rafael and Hennessy, Matthew and Eidenbenz, Stephan and Conejo, Ricardo}, year = {2002}, series = {Lecture Notes in Computer Science}, volume = {2380}, pages = {950--961}, publisher = {Springer}, address = {Berlin}, note = {29th International Colloquium, ICALP, M{\'{a}}laga, Spain, July 8--13, 2002} } @Article{Bra02c, author = {Brattka, Vasco}, title = {Some notes on {F}ine computability}, journal = {Journal of Universal Computer Science}, year = {2002}, volume = {8}, number = {3}, pages = {382--395} } @InProceedings{Bra02d, author = {Brattka, Vasco}, title = {Computing Uniform Bounds}, booktitle = {{CCA} 2002 Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus}, year = {2002}, series = {Electronic Notes in Theoretical Computer Science}, volume = {66}, publisher = {Elsevier}, address = {Amsterdam}, note = {5th International Workshop, CCA 2002, M{\'{a}}laga, Spain, July 12--13, 2002} } @InCollection{Bra03, author = {Brattka, Vasco}, title = {Computability over Topological Structures}, booktitle = {Computability and Models}, editor = {Cooper, S. Barry and Goncharov, Sergey S.}, year = {2003}, pages = {93--136}, publisher = {Kluwer Academic Publishers}, address = {New York} } @InProceedings{Bra03b, author = {Brattka, Vasco}, title = {The Inversion Problem for Computable Linear Operators}, booktitle = {STACS 2003}, editor = {Alt, Helmut and Habib, Michel}, year = {2003}, series = {Lecture Notes in Computer Science}, volume = {2607}, pages = {391--402}, publisher = {Springer}, address = {Berlin}, note = {20th Annual Symposium on Theoretical Aspects of Computer Science, Berlin, Germany, February 27--March 1, 2003} } @Article{Bra03c, author = {Brattka, Vasco}, title = {Effective Representations of the Space of Linear Bounded Operators}, journal = {Applied General Topology}, year = {2003}, volume = {4}, number = {1}, pages = {115--131} } @TechReport{Bra03d, author = {Brattka, Vasco}, title = {Plottable real number functions and the computable graph theorem}, year = {2003}, month = {July}, number = {300}, type = {Informatik Berichte}, institution = {FernUniversit\"at in Hagen, Fachbereich Informatik}, address = {Hagen} } @Article{Bra03e, author = {Brattka, Vasco}, title = {Recursive Quasi-Metric Spaces}, journal = {Theoretical Computer Science}, year = {2003}, volume = {305}, pages = {17--42} } @InProceedings{Bra03f, author = {Brattka, Vasco}, title = {The Emperor's New Recursiveness: The Epigraph of the Exponential Function in Two Models of Computability}, booktitle = {Words, Languages \& Combinatorics III}, editor = {Ito, Masami and Imaoka, Teruo}, year = {2003}, pages = {63--72}, publisher = {World Scientific Publishing}, address = {Singapore}, note = {ICWLC 2000, Kyoto, Japan, March 14--18, 2000} } @TechReport{Bra03i, author = {Brattka, Vasco}, title = {Computability on Asymmetric Spaces}, year = {2003}, month = {December}, number = {305}, type = {Informatik Berichte}, institution = {FernUniversit\"at in Hagen, Fachbereich Informatik}, address = {Hagen} } @InCollection{Bra04, author = {Brattka, Vasco}, title = {Du 13-i{\`e}me probl{\`e}me de {H}ilbert {\`a} la th{\'e}orie des r{\'e}seaux de neurones : aspects constructifs du th{\'e}or{\`e}me de superposition de {K}olmogorov}, booktitle = {L'h{\'e}ritage de {K}olmogorov en math{\'e}matiques}, editor = {Charpentier, {\'E}ric and Lesne, Annick and Nikolski, Nikola${\ddot{\i}}$}, year = {2004}, pages = {241--268}, publisher = {{\'E}ditions Belin}, address = {Paris} } @Article{Bra05, author = {Brattka, Vasco}, title = {Effective {B}orel measurability and reducibility of functions}, journal = {Mathematical Logic Quarterly}, year = {2005}, volume = {51}, number = {1}, pages = {19--44} } @InProceedings{Bra05a, author = {Brattka, Vasco}, title = {On the {B}orel Complexity of {H}ahn-{B}anach Extensions}, booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus}, year = {2005}, series = {Electronic Notes in Theoretical Computer Science}, volume = {120}, pages = {3--16}, publisher = {Elsevier}, address = {Amsterdam}, note = {6th International Workshop, CCA 2004, Wittenberg, Germany, August 16--20, 2004} } @InProceedings{Bra05b, author = {Braverman, Mark}, title = {Hyperbolic {J}ulia Sets are Poly-Time Computable}, booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus}, year = {2005}, series = {Electronic Notes in Theoretical Computer Science}, volume = {120}, pages = {17--30}, publisher = {Elsevier}, address = {Amsterdam}, note = {6th International Workshop, CCA 2004, Wittenberg, Germany, August 16--20, 2004} } @InCollection{Bra05d, author = {Brattka, Vasco}, title = {Computability on Non-Separable {B}anach Spaces and {L}andau's Theorem}, booktitle = {From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive Mathematics}, editor = {Crosilla, Laura and Schuster, Peter}, year = {2005}, pages = {316--333}, publisher = {Oxford University Press} } @InProceedings{Bra06, author = {Brattka, Vasco}, title = {Computable Versions of the Uniform Boundedness Theorem}, booktitle = {Logic Colloquium 2002}, editor = {Chatzidakis, Z. and Koepke, P. and Pohlers, W.}, year = {2006}, series = {Lecture Notes in Logic}, volume = {27}, pages = {130--151}, publisher = {Association for Symbolic Logic}, address = {Urbana} } @Article{Bra06a, author = {Braverman, Mark}, title = {Parabolic {J}ulia sets are polynomial time computable}, journal = {Nonlinearity}, year = {2006}, volume = {19}, number = {6}, pages = {1383--1401} } @InCollection{Bra07, author = {Brattka, Vasco}, title = {From {H}ilbert's 13th {P}roblem to the theory of neural networks: constructive aspects of {K}olmogorov's {S}uperposition {T}heorem}, booktitle = {Kolmogorov's Heritage in Mathematics}, editor = {Charpentier, {\'E}ric and Lesne, Annick and Nikolski, Nikola${\ddot{\i}}$}, year = {2007}, pages = {253--280}, publisher = {Springer}, address = {Berlin} } @Article{Bra08, author = {Brattka, Vasco}, title = {Plottable real number functions and the computable graph theorem}, journal = {SIAM Journal on Computing}, year = {2008}, volume = {38}, number = {1}, pages = {303--328} } @Article{Bra08b, author = {Brattka, Vasco}, title = {Borel Complexity and Computability of the {H}ahn-{B}anach {T}heorem}, journal = {Archive for Mathematical Logic}, year = {2008}, volume = {46}, number = {7--8}, pages = {547--564} } @InProceedings{Bra95, author = {Brattka, Vasco}, title = {Computable selection in analysis}, booktitle = {Computability and Complexity in Analysis}, editor = {Ko, Ker-I and Weihrauch, Klaus}, year = {1995}, month = {September}, series = {Informatik Berichte}, volume = {190}, pages = {125--138}, publisher = {FernUniversit\"at Hagen}, note = {CCA Workshop, Hagen, August 19--20, 1995} } @Article{Bra96, author = {Brattka, Vasco}, title = {Recursive characterization of computable real-valued functions and relations}, journal = {Theoretical Computer Science}, year = {1996}, volume = {162}, pages = {45--77} } @Article{Bra97, author = {Brattka, Vasco}, title = {Order-free Recursion on the Real Numbers}, journal = {Mathematical Logic Quarterly}, year = {1997}, volume = {43}, pages = {216--234} } @PhdThesis{Bra98b, author = {Brattka, Vasco}, title = {Recursive and Computable Operations over Topological Structures}, year = {1998}, school = {Fachbereich Informatik}, address = {FernUniversit\"{a}t Hagen} } @Article{Bra99, author = {Brattka, Vasco}, title = {Computable invariance}, journal = {Theoretical Computer Science}, year = {1999}, volume = {210}, pages = {3--20} } @InProceedings{Bra99a, author = {Brattka, Vasco}, title = {A Stability Theorem for Recursive Analysis}, booktitle = {Combinatorics, Computation \& Logic}, editor = {Cristian S. Calude and Michael J. Dinneen}, year = {1999}, series = {Discrete Mathematics and Theoretical Computer Science}, pages = {144--158}, publisher = {Springer}, address = {Singapore}, note = {Proceedings of DMTCS'99 and CATS'99, Auckland, New Zealand, January 1999} } @Article{Bri00, author = {Bridges, Douglas}, title = {Converses of {B}ishop's lemma on located sets}, journal = {Indagationes Mathematicae}, year = {2000}, volume = {11}, number = {1}, pages = {31--38} } @Article{Bri00a, author = {Bridges, Douglas}, title = {A constructive look at functions of bounded variation}, journal = {Bull. London Math. Soc.}, year = {2000}, volume = {32}, number = {3}, pages = {316--324} } @Article{Bri00b, author = {Bridges, Douglas}, title = {Constructive methods in {B}anach algebra theory}, journal = {Mathematica Japonica}, year = {2000}, volume = {52}, number = {1}, pages = {145--161} } @Article{Bri01, author = {Bridges, Douglas}, title = {Prime and maximal ideals in constructive ring theory}, journal = {Communications in Algebra}, year = {2001}, volume = {29}, number = {7}, pages = {2787--2803} } @InProceedings{Bri01a, author = {Bridges, Douglas}, title = {Dini's Theorem: A Constructive Case Study}, booktitle = {Combinatorics, Computability and Logic}, editor = {Calude, C.S. and Dinneen, M.J. and Sburlan, S.}, year = {2001}, series = {Discrete Mathematics and Theoretical Computer Science}, pages = {69--80}, publisher = {Springer}, address = {London}, note = {Proceedings of DMTCS 2001} } @Article{Bri02, author = {Bridges, Douglas}, title = {Reality and virtual reality in mathematics}, journal = {Bulletin of the European Association for Theoretical Computer Science}, year = {2002}, volume = {78}, pages = {221--230} } @InProceedings{Bri03, author = {Bridges, Douglas S.}, title = {First steps in constructive game theory}, booktitle = {Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning}, year = {2003}, month = {August}, series = {Informatik Berichte}, volume = {302}, pages = {3--9}, publisher = {FernUniversit\"at in Hagen}, note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003} } @Article{Bri04, author = {Bridges, Douglas S.}, title = {First steps in constructive game theory}, journal = {Mathematical Logic Quarterly}, year = {2004}, volume = {50}, number = {4,5}, pages = {501--506} } @Article{Bri04a, author = {Bridges, Douglas S.}, title = {Constructivity in mathematics}, journal = {Cubo}, year = {2004}, volume = {6}, number = {1}, pages = {209--258} } @Article{Bri04b, author = {Bridges, Douglas S.}, title = {Constructive complements of unions of two closed sets}, journal = {Mathematical Logic Quarterly}, year = {2004}, volume = {50}, number = {3}, pages = {293--294} } @InCollection{Bri06, author = {Bridges, Douglas S.}, title = {{C}hurch's thesis and {B}ishop's constructivism}, booktitle = {{C}hurch's Thesis After 70 Years}, editor = {Olszewski, Adam}, year = {2006}, pages = {58--65}, publisher = {Ontos}, address = {Berlin} } @InProceedings{Bri07, author = {Bridges, Douglas S.}, title = {Colocatedness and {L}ebesgue Integrability}, booktitle = {Computation and Logic in the Real World}, editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea}, year = {2007}, series = {Lecture Notes in Computer Science}, volume = {4497}, pages = {98--104}, publisher = {Springer}, address = {Berlin}, note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007} } @Article{Bri07a, author = {Bridges, Douglas S.}, title = {Constructing local optima on a compact interval}, journal = {Archive for Mathematical Logic}, year = {2007}, volume = {46}, pages = {149--154} } @InCollection{Bri07b, author = {Bridges, Douglas S.}, title = {Philosophy of mathematics: 5 questions}, booktitle = {Philosophy of mathematics: 5 questions}, editor = {Hendricks, Vincent F. and Leitgeb, Hannes}, year = {2007}, pages = {45--49}, publisher = {Automatic Press/VIP}, address = {New York, London} } @Article{Bri07c, author = {Briseid, Eyvind}, title = {A rate of convergence for asymptotic contractions}, journal = {J. Math. Anal. Appl.}, year = {2007}, volume = {330}, pages = {364--376} } @Article{Bri07d, author = {Briseid, Eyvind}, title = {Some results on {K}irk's asymptotic contractions}, journal = {Fixed Point Theory}, year = {2007}, volume = {8}, pages = {17--27} } @Article{Bri08, author = {Bridges, Douglas S.}, title = {Uniform continuity properties of preference relations}, journal = {Notre Dame Journal of Formal Logic}, year = {2008}, volume = {49}, number = {1}, pages = {97--106} } @Article{Bri08a, author = {Bridges, Douglas S.}, title = {Product a-frames and proximity}, journal = {Mathematical Logic Quarterly}, year = {2008}, volume = {54}, number = {1}, pages = {12--25} } @Article{Bri76, author = {Bridges, Douglas S.}, title = {Some notes on continuity in constructive analysis}, journal = {Bull. London Math. Soc.}, year = {1976}, volume = {8}, number = {2}, pages = {179--182} } @Article{Bri77, author = {Bridges, Douglas S.}, title = {A constructive look at orthonormal bases in {H}ilbert space}, journal = {Amer. Math. Monthly}, year = {1977}, volume = {84}, number = {3}, pages = {189--191} } @Article{Bri77a, author = {Bridges, Douglas S.}, title = {The constructive {R}adon-{N}ikod\'ym theorem}, journal = {Pacific J. Math.}, year = {1977}, volume = {70}, number = {1}, pages = {51--65} } @Article{Bri78, author = {Bridges, Douglas S.}, title = {A note on {M}orse's lambda-notation in set theory}, journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik}, year = {1978}, volume = {24}, number = {2}, pages = {113--114} } @Article{Bri78a, author = {Bridges, Douglas S.}, title = {On weak operator compactness of the unit ball of ${L}({H})$}, journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik}, year = {1978}, volume = {24}, number = {6}, pages = {493--494} } @Article{Bri78b, author = {Bridges, Douglas S.}, title = {On the connectivity of convex sets}, journal = {The Bulletin of the London Mathematical Society}, year = {1978}, volume = {10}, number = {1}, pages = {86--90} } @Article{Bri78c, author = {Bridges, Douglas S.}, title = {On continuous mappings between locally compact metric spaces}, journal = {The Bulletin of the London Mathematical Society}, year = {1978}, volume = {10}, number = {2}, pages = {201--208} } @Article{Bri78d, author = {Bridges, D. S.}, title = {More on the connectivity of convex sets}, journal = {Proceedings of the American Mathematical Society}, year = {1978}, volume = {68}, number = {2}, pages = {214--216} } @Book{Bri79, author = {Bridges, Douglas S.}, title = {Constructive Functional Analysis}, year = {1979}, publisher = {Pitman}, address = {London} } @Article{Bri79a, author = {Bridges, Douglas S.}, title = {Connectivity properties of metric spaces}, journal = {Pacific Journal of Mathematics}, year = {1979}, volume = {80}, number = {2}, pages = {325--331} } @Article{Bri79b, author = {Bridges, Douglas S.}, title = {On the constructive convergence of series of independent functions}, journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik}, year = {1979}, volume = {25}, number = {1}, pages = {93--96} } @Article{Bri79c, author = {Bridges, Douglas S.}, title = {A criterion for compactness in metric spaces?}, journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik}, year = {1979}, volume = {25}, number = {2}, pages = {97--98} } @Article{Bri79d, author = {Bridges, Douglas S.}, title = {Geometric intuition and elementary constructive analysis}, journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik}, year = {1979}, volume = {25}, number = {6}, pages = {521--523} } @Article{Bri80, author = {Bridges, Douglas S.}, title = {On the foundations of best-approximation theory}, journal = {Journal of Approximation Theory}, year = {1980}, volume = {28}, number = {3}, pages = {273--292} } @Article{Bri80a, author = {Bridges, Douglas S.}, title = {A constructive development of {C}hebyshev approximation theory}, journal = {Journal of Approximation Theory}, year = {1980}, volume = {30}, number = {2}, pages = {99--120} } @InProceedings{Bri81, author = {Bridges, Douglas S.}, title = {Towards a constructive foundation for quantum mechanics}, booktitle = {Constructive Mathematics}, editor = {Richman, F.}, year = {1981}, series = {Lecture Notes in Mathematics}, volume = {873}, pages = {260--273}, note = {Proc. New Mexico State Univ. Conf., Aug. 11--15, 1980, Las Cruces, NM} } @Article{Bri81a, author = {Bridges, Douglas S.}, title = {A constructive look at positive linear functionals on ${\cal{L}}({H})$}, journal = {Pacific Journal of Mathematics}, year = {1981}, volume = {95}, number = {1}, pages = {11--25} } @Article{Bri81b, author = {Bridges, Douglas S.}, title = {On the isolation of zeroes of an analytic function}, journal = {Pacific Journal of Mathematics}, year = {1981}, volume = {96}, number = {1}, pages = {13--22} } @Article{Bri81c, author = {Bridges, Douglas S.}, title = {Correction to: ``{O}n the isolation of zeroes of an analytic function''\ [{P}acific {J}. {M}ath. {\bf 96} (1981), no. 1, 13--22; {M}{R} 82k:03095]}, journal = {Pacific Journal of Mathematics}, year = {1981}, volume = {97}, number = {2}, pages = {487--488} } @Article{Bri81d, author = {Bridges, Douglas S.}, title = {A constructive analysis of the {R}emes algorithm}, journal = {Journal of Approximation Theory}, year = {1981}, volume = {32}, number = {4}, pages = {257--270} } @Article{Bri81e, author = {Bridges, Douglas S.}, title = {A constructive proximinality property of finite-dimensional linear subspaces}, journal = {The Rocky Mountain Journal of Mathematics}, year = {1981}, volume = {11}, number = {4}, pages = {491--497} } @Article{Bri81f, author = {Bridges, Douglas S.}, title = {On {M}ontel's proof of the great {P}icard theorem}, journal = {The American Mathematical Monthly}, year = {1981}, volume = {88}, number = {1}, pages = {45--47} } @Article{Bri82, author = {Bridges, Douglas S.}, title = {Preference and utility: a constructive development}, journal = {Journal of Mathematical Economics}, year = {1982}, volume = {9}, number = {1-2}, pages = {165--185} } @Article{Bri82a, author = {Bridges, Douglas S.}, title = {Lipschitz constants and moduli of continuity for the {C}hebyshev projection}, journal = {Proceedings of the American Mathematical Society}, year = {1982}, volume = {85}, number = {4}, pages = {557--561} } @InCollection{Bri82b, author = {Bridges, Douglas S.}, title = {Recent progress in constructive approximation theory}, booktitle = {The L. E. J. Brouwer Centenary Symposium (Noordwijkerhout, 1981)}, year = {1982}, pages = {41--50}, publisher = {North-Holland}, address = {Amsterdam} } @Article{Bri83, author = {Bridges, Douglas S.}, title = {Numerical representation of intransitive preferences on a countable set}, journal = {Journal of Economic Theory}, year = {1983}, volume = {30}, number = {1}, pages = {213--217} } @Article{Bri83a, author = {Bridges, Douglas S.}, title = {A numerical representation of preferences with intransitive indifference}, journal = {Journal of Mathematical Economics}, year = {1983}, volume = {11}, number = {1}, pages = {25--42} } @Article{Bri85, author = {Bridges, Douglas S.}, title = {Representing interval orders by a single real-valued function}, journal = {Journal of Economic Theory}, year = {1985}, volume = {36}, number = {1}, pages = {149--155} } @Article{Bri85a, author = {Bridges, Douglas S.}, title = {Operator ranges, integrable sets, and the functional calculus}, journal = {Houston Journal of Mathematics}, year = {1985}, volume = {11}, number = {1}, pages = {31--44} } @Article{Bri86, author = {Bridges, Douglas S.}, title = {Numerical representation of interval orders on a topological space}, journal = {Journal of Economic Theory}, year = {1986}, volume = {38}, number = {1}, pages = {160--166} } @InCollection{Bri87, author = {Bridges, Douglas S.}, title = {A constructive {M}orse theory of sets}, booktitle = {Mathematical logic and its applications (Druzhba, 1986)}, year = {1987}, pages = {61--79}, publisher = {Plenum}, address = {New York} } @Article{Bri88, author = {Bridges, Douglas S.}, title = {Locatedness, convexity, and Lebesque measurability}, journal = {Quart. J. Math. Oxford Ser. 2}, year = {1988}, volume = {39}, pages = {411--421} } @Article{Bri88a, author = {Bridges, Douglas S.}, title = {The {E}uclidean distance construction of order homomorphisms}, journal = {Mathematical Social Sciences}, year = {1988}, volume = {15}, number = {2}, pages = {179--188} } @Article{Bri89, author = {Bridges, Douglas S.}, title = {A general constructive intermediate value theorem}, journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik}, year = {1989}, volume = {35}, pages = {433--435} } @Article{Bri89a, author = {Bridges, Douglas S.}, title = {The constructive theory of preference relations on a locally compact space}, journal = {Indagationes Mathematicae}, year = {1989}, volume = {51}, number = {2}, pages = {141--165} } @Article{Bri89b, author = {Bridges, Douglas S.}, title = {Approximate interpolation by functions in a {H}aar space}, journal = {Journal of Approximation Theory}, year = {1989}, volume = {57}, number = {1}, pages = {35--39} } @Article{Bri90, author = {Bridges, Douglas S.}, title = {Preference, indifference, and {M}arkov's principle}, journal = {Mathematical Social Sciences}, year = {1990}, volume = {20}, number = {2}, pages = {131--145} } @InCollection{Bri90a, author = {Bridges, Douglas S.}, title = {Order isomorphisms---a constructive measure-theoretic view}, booktitle = {Mathematical logic}, year = {1990}, pages = {243--255}, publisher = {Plenum}, address = {New York} } @Article{Bri91, author = {Bridges, Douglas S.}, title = {The constructive inequivalence of various notions of preference ordering}, journal = {Mathematical Social Sciences}, year = {1991}, volume = {21}, number = {2}, pages = {169--176} } @Article{Bri93, author = {Bridges, Douglas S.}, title = {Sequential, pointwise, and uniform continuity: a constructive note}, journal = {Mathematical Logic Quarterly}, year = {1993}, volume = {39}, number = {1}, pages = {55--61} } @Article{Bri93a, author = {Bridges, Douglas S.}, title = {Constructive notions of strict convexity}, journal = {Mathematical Logic Quarterly}, year = {1993}, volume = {39}, number = {3}, pages = {295--300} } @InCollection{Bri94a, author = {Bridges, Douglas S.}, title = {A constructive look at the real number line}, booktitle = {Real numbers, generalizations of the reals, and theories of continua}, year = {1994}, pages = {29--92}, publisher = {Kluwer Acad. Publ.}, address = {Dordrecht} } @Article{Bri94b, author = {Bridges, Douglas S.}, title = {The constructive theory of preference relations on a locally compact space. {I}{I}}, journal = {Mathematical Social Sciences}, year = {1994}, volume = {27}, number = {1}, pages = {1--9} } @Article{Bri95, author = {Bridges, Douglas S.}, title = {Constructive mathematics and unbounded operations}, journal = {J. Philos. Logic}, year = {1995}, volume = {24}, number = {5}, pages = {549--561} } @InProceedings{Bri98, author = {Bridges, Douglas S.}, title = {Bishop's Principle}, booktitle = {Computability and Complexity in Analysis}, editor = {Ko, Ker-I and Nerode, Anil and Pour-El, Marian B. and Weihrauch, Klaus and Wiedermann, Ji{\v{r}}{\'{\i}}}, year = {1998}, month = {August}, series = {Informatik Berichte}, volume = {235}, pages = {17--20}, publisher = {FernUniversit\"at Hagen}, note = {CCA Workshop, Brno, Czech Republic, August, 1998} } @InCollection{Bri98a, author = {Bridges, Douglas S.}, title = {Constructive truth in practice}, booktitle = {Truth in mathematics (Mussomeli, 1995)}, year = {1998}, pages = {53--69}, publisher = {Oxford Univ. Press}, address = {New York} } @Article{Bri99, author = {Bridges, Douglas S.}, title = {Constructive mathematics: a foundation for computable analysis}, journal = {Theoretical Computer Science}, year = {1999}, volume = {219}, pages = {95--109} } @Article{Bri99a, author = {Bridges, Douglas S.}, title = {Can constructive mathematics be applied in physics?}, journal = {Journal of Philosophical Logic}, year = {1999}, volume = {28}, number = {5}, pages = {439--453} } @InCollection{Bri99b, author = {Bridges, Douglas S.}, title = {Constructive methods in mathematical economics}, booktitle = {Mathematical utility theory (Essen, 1997)}, editor = {Herden, Gerhard and Knoche, Norbert and Seidl, Christian and Trockel, Walter}, year = {1999}, series = {Journal of Economy}, volume = {Supp. 8}, pages = {1--21}, publisher = {Springer}, address = {Vienna} } @InProceedings{Bro07, author = {Brodhead, Paul}, title = {Enumerations of {$\Pi^0_1$} classes: acceptability and decidable classes}, booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis}, editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus}, year = {2007}, series = {Electronic Notes in Theoretical Computer Science}, volume = {167}, pages = {289--301}, publisher = {Elsevier}, address = {Amsterdam}, note = {CCA 2006, Gainesville, Florida, USA, November 1--5, 2006} } @Article{Bro25, author = {Brouwer, L.E.J.}, title = {Intuitionistischer {B}eweis des {J}ordanschen {K}urvensatzes}, journal = {Koninklijke Nederl. Akad. Wentensch, Proc.}, year = {1925}, volume = {28}, pages = {503--508}, note = {translated in: A. Heyting (ed.), Collected Works, Vol. 1, Philosophy and Foundations of Mathematics, North-Holland, Amsterdam, 1975, 315--320} } @Article{Bro52, author = {Brouwer, L.E.J.}, title = {An intuitionist correction of the fixed-point theorem on the sphere}, journal = {Proc. Roy. Soc. London, Ser. A}, year = {1952}, volume = {213}, pages = {1--2} } @Article{Bro54, author = {Brouwer, L.E.J.}, title = {Points and spaces}, journal = {Canad. Journ. Math.}, year = {1954}, volume = {6}, pages = {1--17} } @InProceedings{Bro75, author = {Brouwer, L.E.J.}, title = {The unreliability of logical principles}, booktitle = {Collected Works, Vol. 1, Philosophy and Foundations of Mathematics}, editor = {Heyting, A.}, year = {1975}, pages = {107--111}, publisher = {North-Holland}, address = {Amsterdam} } @InProceedings{Bro75a, author = {Brouwer, L.E.J.}, title = {Fixed cores which cannot be found, though they are claimed to exist by classical theorems}, booktitle = {Collected Works, Vol. 1, Philosophy and Foundations of Mathematics}, editor = {Heyting, A.}, year = {1975}, pages = {516--518}, publisher = {North-Holland}, address = {Amsterdam} } @Book{Bro75b, author = {Brouwer, L.E.J.}, title = {Collected Works, Vol. 1, Philosophy and Foundations of Mathematics}, year = {1975}, publisher = {North-Holland}, address = {Amsterdam}, note = {Heyting, A. (ed)} } @Book{Bro75c, author = {Brouwer, L.E.J.}, title = {Collected Works, Vol. 2, Geometry, Analysis, Topology and Mechanics}, year = {1976}, publisher = {North-Holland}, address = {Amsterdam}, note = {Freudenthal, H. (ed)} } @Book{Bro81, author = {Brouwer, L.E.J.}, title = {Brouwer's Cambridge Lectures on Intuitionism}, year = {1981}, publisher = {Cambridge Univ. Press}, note = {van Dalen, D. (ed)} } @InProceedings{Buy00, author = {Buy, Dmitry}, title = {Some Remarks about Fixpoint Theorems}, booktitle = {Computability and Complexity in Analysis}, editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter and Weihrauch, Klaus}, year = {2000}, month = {September}, series = {Informatik Berichte}, volume = {272}, pages = {43--52}, publisher = {FernUniversit\"at Hagen}, note = {CCA 2000 Workshop, Swansea, Wales, September 17--19, 2000} } @InProceedings{CCHK99, author = {Calude, C. S. and Coles, R. and Hertling, P. H. and Khoussainov, B.}, title = {Degree Theoretic Aspects of Computably Enumerable Reals}, booktitle = {Models and Computability}, editor = {S. B. Cooper and J. K. Truss}, year = {1999}, series = {London Math.\ Society Lecture Note Series}, volume = {259}, pages = {23--39}, publisher = {Cambridge University Press}, address = {Cambridge}, note = {Invited Papers from {L}ogic {C}olloquium 1997, {L}eeds.} } @Proceedings{CDGW07, title = {Proceedings of the Third International Conference on Computability and Complexity in Analysis}, editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus}, year = {2007}, series = {Electronic Notes in Theoretical Computer Science}, volume = {167}, publisher = {Elsevier}, address = {Amsterdam}, note = {CCA 2006, Gainesville, Florida, USA, November 1--5, 2006} } @InProceedings{CDK08, author = {Cenzer, Douglas and Dashti, S. Ali and King, Jonathan L.~F.}, title = {Effective Symbolic Dynamics}, booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)}, editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning}, year = {2008}, series = {Electronic Notes in Theoretical Computer Science}, volume = {202}, pages = {89--99}, publisher = {Elsevier}, note = {CCA 2007, Siena, Italy, June 16--18, 2007} } @InProceedings{CG00, author = {Ciaffaglione, Alberto and Di Gianantonio, Pietro}, title = {A Co-inductive Approach to Real Numbers}, booktitle = {Types for Proofs and Programs}, editor = {Coquand, Thierry and Dybjer, Peter and Nordstr{\"{o}}m, Bengt and Smith, Jan}, year = {2000}, series = {Lecture Notes in Computer Science}, volume = {1956}, pages = {114--130}, publisher = {Springer}, address = {Berlin}, note = {International Workshop, TYPES'99, L{\"{o}}keberg, Sweden, June 12--16, 1999} } @InProceedings{CG02, author = {Ciaffaglione, Alberto and Di Gianantonio, Pietro}, title = {A Tour with Constructive Real Numbers}, booktitle = {Types for Proofs and Programs}, editor = {Callaghan, P. and Luo, Z. and McKinna, J. and Pollack, R.}, year = {2002}, series = {LNCS}, volume = {2277}, pages = {41--52}, publisher = {Springer}, address = {Berlin}, note = {International Workshop, TYPES 2000, Durham, UK, December 8--12, 2000} } @Article{CG06, author = {Ciaffaglione, Alberto and Di Gianantonio, Pietro}, title = {A certified, corecursive implementation of exact real numbers}, journal = {Theoretical Computer Science}, year = {2006}, volume = {351}, number = {1}, pages = {39--51} } @InProceedings{CH07, author = {Cenzer, Douglas and Hinman, Peter G.}, title = {{M}edvedev degrees of generalized r.e. separating classes}, booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis}, editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus}, year = {2007}, series = {Electronic Notes in Theoretical Computer Science}, volume = {167}, pages = {203--223}, publisher = {Elsevier}, address = {Amsterdam}, note = {CCA 2006, Gainesville, Florida, USA, November 1--5, 2006} } @Article{CH98, author = {Calude, Cristian S. and Hertling, Peter}, title = {Computable approximations of reals: An information-theoretic analysis}, journal = {Fundamenta Informaticae}, year = {1998}, volume = {33}, number = {2}, pages = {105--120} } @Article{CH99, author = {Chadzelek, Thomas and Hotz, G{\"u}nter}, title = {Analytic machines}, journal = {Theoretical Computer Science}, year = {1999}, volume = {219}, pages = {151--167} } @Article{CHJW01, author = {Calude, C.S. and Hertling, P. and J{\"u}rgensen, H. and Weihrauch, K.}, title = {Randomness on Full Shift Spaces}, journal = {Chaos, Solitons \& Fractals}, year = {2001}, volume = {12}, number = {3}, pages = {491--503} } @Article{CHK97, author = {Calude, Cristian S. and Hertling, Peter and Khoussainov, Bakhadyr}, title = {Do the Zeros of {R}iemann's {Z}eta-Function Form a Random Sequence?}, journal = {Bulletin of the European Association for Theoretical Computer Science}, year = {1997}, volume = {62}, pages = {199--207} } @Article{CHKW01, author = {Calude, Cristian S. and Hertling, Peter H. and Khoussainov, Bakhadyr and Wang, Yongge}, title = {Recursively enumerable reals and {C}haitin $\Omega$ numbers}, journal = {Theoretical Computer Science}, year = {2001}, volume = {255}, pages = {125--149} } @InProceedings{CHKW98, author = {Calude, Cristian S. and Hertling, Peter and Khoussainov, Bakhadyr and Yongge Wang}, title = {Recursively enumerable reals and {C}haitin $\Omega$ numbers}, booktitle = {STACS'98}, editor = {Morvan, Michel et al.}, year = {1998}, series = {Lecture Notes in Computer Science}, volume = {1373}, pages = {596--606}, publisher = {Springer}, address = {Berlin}, note = {15th Annual Symposium on Theoretical Aspects of Computer Science. Paris, France, February 25--27, 1998} } @InProceedings{CJ94, author = {Calude, Cristian and J\"{u}rgensen, Helmut}, title = {Randomness as an invariant for number representations}, booktitle = {Results and Trends in Theoretical Computer Science}, editor = {Maurer, H. and Karhum{\"a}ki, J. and Rozenberg, G.}, year = {1994}, pages = {44--66}, publisher = {Springer}, address = {Berlin} } @Article{CK04, author = {Chou, Arthur W. and Ko, Ker-I}, title = {On the complexity of finding paths in a two-dimensional domain {I}: Shortest paths}, journal = {Mathematical Logic Quarterly}, year = {2004}, volume = {50}, number = {6}, pages = {551--572} } @InProceedings{CK05, author = {Chou, Arthur W. and Ko, Ker-I}, title = {On the complexity of finding paths in a two-dimensional domain {II}: Picewise straight-line paths}, booktitle = {Proceedings of the 6th Workshop on Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Staiger, Ludwig and Weihrauch, Klaus}, year = {2005}, series = {Electronic Notes in Theoretical Computer Science}, volume = {120}, pages = {45--57}, publisher = {Elsevier}, address = {Amsterdam}, note = {6th International Workshop, CCA 2004, Wittenberg, Germany, August 16--20, 2004} } @Article{CK05a, author = {Chou, Arthur W. and Ko, Ker-I}, title = {The computational complexity of distance functions of two-dimensional domains}, journal = {Theoretical Computer Science}, year = {2005}, volume = {337}, pages = {360--369} } @Article{CK95, author = {Chou, Arthur and Ko, Ker-I}, title = {Computational complexity of two-dimensional regions}, journal = {SIAM Journal on Computing}, year = {1995}, volume = {24}, pages = {923--947} } @Article{CL06, author = {Chernavskya, A.V. and Leksineb, V.P.}, title = {Unrecognizability of manifolds}, journal = {Annals of Pure and Applied Logic}, year = {2006}, volume = {141}, number = {3}, pages = {447--455} } @InProceedings{CLM07, author = {Costa, Jos\'{e} F\'{e}lix and Loff, Bruno and Mycka, Jerzy}, title = {The New Promise of Analog Computation}, booktitle = {Computation and Logic in the Real World}, editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea}, year = {2007}, series = {Lecture Notes in Computer Science}, volume = {4497}, pages = {189--195}, publisher = {Springer}, address = {Berlin}, note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007} } @InProceedings{CM01, author = {Campagnolo, Manuel Lameiras and Moore, Cristopher}, title = {Upper and lower bounds on continuous-time computation}, booktitle = {Unconventional Models of Computation, UMC2'K}, editor = {Antoniou, I. and Calude, C.S. and Dinneen, M.J.}, year = {2001}, series = {Discrete Mathematics and Theoretical Computer Science}, pages = {135--153}, publisher = {Springer}, address = {London}, note = {Second International Conference, UMC 2000, Brussels, Belgium} } @Article{CMC01, author = {Campagnolo, Manuel Lameiras and Moore, Cristopher and Costa, Jos\'{e} F\'{e}lix}, title = {Iteration, Inequalities, and Differentiability in Analog Computers}, journal = {Journal of Complexity}, year = {2001}, volume = {16}, number = {4}, pages = {642--660} } @Article{CMC02, author = {Campagnolo, Manuel Lameiras and Moore, Cristopher and Costa, Jos\'{e} F\'{e}lix}, title = {An Analog Characterization of the {G}rzegorczyk Hierarchy}, journal = {Journal of Complexity}, year = {2002}, volume = {18}, number = {4}, pages = {977--1000} } @InProceedings{CO07, author = {Campagnolo, Manuel L. and Ojakian, Kerry}, title = {The methods of approximation and lifting in real computation}, booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis}, editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus}, year = {2007}, series = {Electronic Notes in Theoretical Computer Science}, volume = {167}, pages = {387--423}, publisher = {Elsevier}, address = {Amsterdam}, note = {CCA 2006, Gainesville, Florida, USA, November 1--5, 2006} } @Article{CO08, author = {Campagnolo, Manuel L. and Ojakian, Kerry}, title = {The elementary computable functions over the real numbers: applying two new techniques}, journal = {Archive for Mathematical Logic}, year = {2008}, volume = {46}, number = {7--8}, pages = {593–-627} } @Article{CP75, author = {Caldwell, J. and Pour-El, Marian Boykan}, title = {On a simple definition of computable functions of a real variable - with applications to functions of a complex variable}, journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik}, year = {1975}, volume = {21}, pages = {1--19} } @Article{CR02, author = {Cenzer, Douglas and Remmel, Jeffrey B.}, title = {Effectively closed sets and graphs of computable real functions}, journal = {Theoretical Computer Science}, year = {2002}, volume = {284}, number = {2}, pages = {279--318} } @Article{CR03, author = {Cenzer, Douglas and Remmel, Jeffrey B.}, title = {Index sets for $\omega$--languages}, journal = {Mathematical Logic Quarterly}, year = {2003}, volume = {49}, number = {1}, pages = {22--33} } @InProceedings{CR03a, author = {Cenzer, Douglas and Remmel, Jeffrey B.}, title = {Index sets for computable real functions}, booktitle = {Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus and Zhong, Ning}, year = {2003}, month = {August}, series = {Informatik Berichte}, volume = {302}, pages = {164--182}, publisher = {FernUniversit\"at in Hagen}, note = {International Conference, CCA 2003, Cincinnati, USA, August 28--30, 2003} } @Article{CR04, author = {Cenzer, Douglas and Remmel, Jeffrey B.}, title = {Index sets for computable differential equations}, journal = {Mathematical Logic Quarterly}, year = {2004}, volume = {50}, number = {4,5}, pages = {329--344} } @InProceedings{CR08, author = {Ciobanu, Gabriel and Rusu, D\u{a}nu\c{t}}, title = {Supermetrics over Apartness Lattice-Ordered Semigroup}, booktitle = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)}, editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning}, year = {2008}, series = {Electronic Notes in Theoretical Computer Science}, volume = {202}, pages = {191--200}, publisher = {Elsevier}, note = {CCA 2007, Siena, Italy, June 16--18, 2007} } @Article{CR99, author = {Cenzer, Douglas and Remmel, Jeffrey B.}, title = {Index sets in computable analysis}, journal = {Theoretical Computer Science}, year = {1999}, volume = {219}, pages = {111--150} } @Article{CS05, author = {Calude, Cristian S. and Staiger, Ludwig}, title = {Generalisations of disjunctive sequences}, journal = {Mathematical Logic Quarterly}, year = {2005}, volume = {51}, number = {2}, pages = {120--128} } @Article{CS07, author = {Cagnard, Benoit and Simonnet, Pierre}, title = {Automata, {B}orel Functions and Real Numbers in {P}isot Base}, journal = {Theoretical Informatics and Applications}, year = {2007}, volume = {41}, number = {1}, pages = {27--44} } @InProceedings{CSZ07, author = {Chen, Qingliang and Su, Kaile and Zheng, Xizhong}, title = {Primitive recursiveness of real numbers under different representation}, booktitle = {Proceedings of the Third International Conference on Computability and Complexity in Analysis}, editor = {Cenzer, Douglas and Dillhage, Ruth and Grubba, Tanja and Weihrauch, Klaus}, year = {2007}, series = {Electronic Notes in Theoretical Computer Science}, volume = {167}, pages = {303--324}, publisher = {Elsevier}, address = {Amsterdam}, note = {CCA 2006, Gainesville, Florida, USA, November 1--5, 2006} } @Article{CSZ07a, author = {Chen, Qingliang and Su, Kaile and Zheng, Xizhong}, title = {Primitive recursive real numbers}, journal = {Mathematical Logic Quarterly}, year = {2007}, volume = {53}, number = {4--5}, pages = {365--380} } @Article{CY83, author = {Collins, W. and Young, P.}, title = {Discountinuities of provably correct operators on the provably recursive real numbers}, journal = {The Journal of Symbolic Logic}, year = {1983}, volume = {48}, pages = {913--920} } @Article{CZ62, author = {Ce{\u{\i}}tin, G.S. and Zaslavski{\u{i}}, I.D.}, title = {Singular coverings and properties of constructive functions connected with them}, journal = {Tr.\ Mat.\ Inst.\ Steklov}, year = {1962}, volume = {67}, pages = {458--502}, note = {(Russian)} } @Article{CZ70, author = {Ce{\u{\i}}tin, G.S. and Zaslavski{\u{i}}, I.D.}, title = {A criterion of the rectifiability of constructive plane curves}, journal = {Izv. {A}kad {N}auk {A}rmjan. SSR Ser. Mat.}, year = {1970}, volume = {5}, pages = {434--440}, note = {(Russian)} } @Article{CZ71, author = {Ce{\u{\i}}tin, G.S. and Zaslavski{\u{i}}, I.D.}, title = {Yet another constructive variant of the {C}auchy theorem}, journal = {{Z}ap. {N}au\v{c}n. {S}em. {L}eningrad. {O}tdel. {M}at. {I}nst. {S}teklov ({L}{O}{M}{I})}, year = {1971}, volume = {20}, pages = {36--39,282--283}, note = {(Russian)} } @InProceedings{CZS68, author = {Ce{\u{\i}}tin, G.S. and Zaslavski{\u{i}} and \v{S}anin N.A.}, title = {Peculiarities of constructive mathematical analysis}, booktitle = {Proc. Internat. Congr. Math.}, year = {1968}, pages = {253--261}, publisher = {Mir}, address = {Moscow}, note = {(Moscow, 1966, in Russian)} } @Article{Cal02, author = {Calude, Cristian S.}, title = {A characterization of c.e. random reals}, journal = {Theoretical Computer Science}, year = {2002}, volume = {271}, pages = {3--14} } @Article{Cal02a, author = {Calude, Cristian S.}, title = {Chaitin $\Omega$ numbers, {S}olovay machines, and {G}{\"{o}}del incompleteness}, journal = {Theoretical Computer Science}, year = {2002}, volume = {284}, number = {2}, pages = {269--277} } @PhdThesis{Cam01, author = {Campagnolo, Manuel Lameiras}, title = {Computational Complexity of Real Valued Recursive Functions and Analog Circuits}, year = {2001}, school = {Instituto Superior T{\'e}cnico, Universidade T{\'e}cnica de Lisboa}, address = {Lisbon} } @InProceedings{Cam02, author = {Campagnolo, Manuel Lameiras}, title = {The Complexity of Real Recursive Functions}, booktitle = {Unconventional Models of Computation}, editor = {Calude, C.S. and Dinneen, M.J. and Peper, F.}, year = {2002}, series = {Lecture Notes in Computer Science}, volume = {2509}, pages = {1--14}, publisher = {Springer}, address = {Berlin}, note = {Third International Conference, UMC 2002, Kobe, Japan, October 15-19, 2002} } @Article{Cei55, author = {Ce{\u{\i}}tin, G.S.}, title = {On a theorem of {C}auchy in constructive analysis}, journal = {Uspehi Mat.\ Nauk}, year = {1955}, volume = {10}, pages = {207--209}, note = {(in Russian)} } @InProceedings{Cei56, author = {Ce{\u{\i}}tin, G.S.}, title = {Uniform recursiveness of algorithmic operators on general recursive functions and a canonical representation for constructive functions of a real argument}, booktitle = {Proc.\ Third All--Union Math.\ Congr., Moscow 1956}, year = {1956}, volume = {1}, pages = {188--189}, publisher = {Izdat.\ Akad.\ Nauk SSSR}, address = {Moscow}, note = {(in Russian)} } @Article{Cei59, author = {Ce{\u{\i}}tin, G.S.}, title = {Algorithmic Operators in Constructive Complete Separable Metric Spaces}, journal = {Doklady Akademii Nauk}, year = {1959}, volume = {128}, pages = {49--52}, note = {(in Russian)} } @Article{Cei62, author = {Ce{\u{\i}}tin, G.S.}, title = {Algorithmic Operators in Constructive Metric Spaces}, journal = {Tr.\ Mat.\ Inst.\ Steklov}, year = {1962}, volume = {67}, pages = {295--361}, note = {(in Russian, English trans. in AMS Trans. 64, 1967)} } @Article{Cei62a, author = {Ce{\u{\i}}tin, G.S.}, title = {Mean value theorems in constructive analysis}, journal = {Tr.\ Mat.\ Inst.\ Steklov}, year = {1962}, volume = {67}, pages = {362--384}, note = {(in Russian, English trans. in AMS Trans. 98, 1971)} } @Article{Cei64, author = {Ce{\u{\i}}tin, G.S.}, title = {Three theorems on constructive functions}, journal = {Tr.\ Mat.\ Inst.\ Steklov}, year = {1964}, volume = {72}, pages = {537--543}, note = {(in Russian, English trans. in AMS Trans. 100, 1972)} } @Article{Cei70, author = {Ce{\u{\i}}tin, G.S.}, title = {On upper bounds of recursively enumerable sets of constructive real numbers}, journal = {Tr.\ Mat.\ Inst.\ Steklov}, year = {1970}, volume = {113}, pages = {102--172}, note = {(in Russian)} } @InProceedings{Cen93, author = {Cenzer, Douglas}, title = {Effective real dynamics}, booktitle = {Logical Methods in Honor of Anil Nerode's Sixtieth Birthday}, editor = {Crossley, John N. and Remmel, Jefferey B. and Shore, Richard A. and Sweedler, Moss E.}, year = {1993}, series = {Progress in Computer Science and Applied Logic}, volume = {12}, pages = {162--177}, publisher = {Birkh\"auser}, address = {Boston} } @Article{Cha87a, author = {Chaitin, G.J.}, title = {Incompleteness theorems for random reals}, journal = {Adv. in Appl. Math.}, year = {1987}, volume = {8}, pages = {119--146} } @PhdThesis{Cha98, author = {Chadzelek, Thomas}, title = {Analytische Maschinen}, year = {1998}, school = {Technische Fakult\"at der Universit\"at des Saarlandes}, address = {Saarbr\"ucken} } @InProceedings{Cho95, author = {Chou, Arthur W.}, title = {Some complexity issues in complex analysis}, booktitle = {Computability and Complexity in Analysis}, editor = {Ko, Ker-I and Weihrauch, Klaus}, year = {1995}, month = {September}, series = {Informatik Berichte}, volume = {190}, pages = {91--98}, publisher = {FernUniversit\"at Hagen}, note = {CCA Workshop, Hagen, August 19--20, 1995} } @Article{Cle69, author = {Cleave, J.P.}, title = {The primitive recursive analysis of ordinary differential equations and the complexity of their solutions}, journal = {Journal of Computer and Systems Sciences}, year = {1969}, volume = {3}, pages = {447--455} } @Article{Col05, author = {Collins, Pieter}, title = {Continuity and computability on reachable sets}, journal = {Theoretical Computer Science}, year = {2005}, volume = {341}, pages = {162--195} } @InProceedings{Col07, author = {Collins, Pieter}, title = {Effective Computation for Nonlinear Systems}, booktitle = {Computation and Logic in the Real World}, editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea}, year = {2007}, series = {Lecture Notes in Computer Science}, volume = {4497}, pages = {169--178}, publisher = {Springer}, address = {Berlin}, note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007} } @Article{Col07a, author = {Collins, Pieter}, title = {Optimal Semicomputable Approximations to Reachable and Invariant Sets}, journal = {Theory of Computing Systems}, year = {2007}, volume = {41}, number = {1}, pages = {33--48} } @Article{Col78, author = {Collins, W.}, title = {Provably recursive real numbers}, journal = {Notre Dame J. Formal Logic}, year = {1978}, volume = {19}, pages = {513--522} } @InProceedings{Coo92, author = {Cook, Stephen A.}, title = {Computability and complexity of higher type functions}, booktitle = {Logic from computer science}, editor = {Moschovakis, Y.N.}, year = {1992}, series = {Mathematical Sciences Research Institute Publications}, volume = {21}, pages = {51--72}, publisher = {Springer}, address = {New York}, note = {Proceedings of the workshop held in Berkeley, California, November 13--17, 1989} } @Article{Coq05, author = {Coquand, Thierry}, title = {Formal Topology and Constructive Mathematics: the {G}elfand and {S}tone-{Y}osida Representation Theorems}, journal = {Journal of Universal Computer Science}, year = {2005}, volume = {11}, number = {12}, pages = {1932--1944} } @Article{Cur03, author = {Curi, Giovanni}, title = {Constructive metrisability in point-free topology}, journal = {Theoretical Computer Science}, year = {2003}, volume = {305}, pages = {85--109} } @InCollection{DB99, author = {Dediu, Lumini{\c{t}}a and Bridges, Douglas}, title = {Constructive notes on uniform and locally convex spaces}, booktitle = {Fundamentals of computation theory}, editor = {Ciobanu, G. and Pun, G.}, year = {1999}, series = {Lecture Notes in Computer Science}, volume = {1684}, pages = {195--203}, publisher = {Springer}, address = {Berlin}, note = {12th International Symposium, FCT'99, Iasi, Romania, August/September 1999} } @InProceedings{DEMY02, author = {Du, Zilin and Eleftheriou, Maria and Moreira, Jos{\'e} E. and Yap, Chee}, title = {Hypergeometric Functions in Exact Geometric Computation}, booktitle = {{CCA} 2002 Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus}, year = {2002}, series = {Electronic Notes in Theoretical Computer Science}, volume = {66}, publisher = {Elsevier}, address = {Amsterdam}, note = {5th International Workshop, CCA 2002, M{\'{a}}laga, Spain, July 12--13, 2002} } @InProceedings{DF87, author = {Demuth, Osvald and Filipec, Pavel}, title = {Differentiation of constructive functions of a real variable and relative computability}, booktitle = {Mathematical Logic and Its Applications}, editor = {Skordev, D.G.}, year = {1987}, pages = {81--106}, publisher = {Plenum Press}, address = {New York}, note = {Proceedings of an advanced international summer school and conference in honor of the 80th anniversary of Kurt G\"odel's birth, held September 24--October 4, 1986 in Druzhba, Bulgaria} } @InProceedings{DG02, author = {Downey, Rod G. and Griffiths, Evan J.}, title = {Schnorr Randomness}, booktitle = {{CCA} 2002 Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus}, year = {2002}, series = {Electronic Notes in Theoretical Computer Science}, volume = {66}, publisher = {Elsevier}, address = {Amsterdam}, note = {5th International Workshop, CCA 2002, M{\'{a}}laga, Spain, July 12--13, 2002} } @Article{DGL04, author = {Downey, Rod G. and Griffiths, Evan J. and LaForte, Geoffrey L.}, title = {On {S}chnorr and computable randomness, martingales, and machines}, journal = {Mathematical Logic Quarterly}, year = {2004}, volume = {50}, number = {6}, pages = {613--627} } @InProceedings{DGS07, author = {de Miguel Casado, Gregorio and Garc{\'{\i}}a Chamizo, Juan Manuel and Signes Pont, Mar{\'{\i}}a Teresa}, title = {Algebraic Model of an Arithmetic Unit for {TTE}-Computable Normalized Rational Numbers}, booktitle = {Computation and Logic in the Real World}, editor = {Cooper, S. Barry and L{\"o}we, Benedikt and Sorbi, Andrea}, year = {2007}, series = {Lecture Notes in Computer Science}, volume = {4497}, pages = {218--227}, publisher = {Springer}, address = {Berlin}, note = {Third Conference on Computability in Europe, CiE 2007, Siena, Italy, June 18-23, 2007} } @Proceedings{DGSWZ08, title = {Proceedings of the Fourth International Conference on Computability and Complexity in Analysis ({CCA} 2007)}, editor = {Dillhage, Ruth and Grubba, Tanja and Sorbi, Andrea and Weihrauch, Klaus and Zhong, Ning}, year = {2008}, series = {Electronic Notes in Theoretical Computer Science}, volume = {202}, address = {Amsterdam}, note = {CCA 2007, Siena, Italy, June 16--18, 2007} } @InProceedings{DHL01, author = {Downey, Rod G. and Hirschfeldt, Denis R. and LaForte, Geoffrey L.}, title = {Randomness and Reducibility}, booktitle = {Mathematical Foundations of Computer Science 2001}, editor = {Sgall, Ji{\v{r}}{\'{\i}} and Pultr, Ale{\v{s}} and Kolman, Petr}, year = {2001}, series = {Lecture Notes in Computer Science}, volume = {2136}, pages = {316--327}, publisher = {Springer}, address = {Berlin}, note = {26th International Symposium, MFCS 2001, Mari{\'{a}}nsk{\'{e}} L{\'{a}}zn{\v{e}}, Czech Republic, August 27-31, 2001} } @InProceedings{DHNS02, author = {Downey, Rod G. and Hirschfeldt, Denis R. and Nies, Andr{\'{e}} and Stephan, Frank}, title = {Trivial Reals}, booktitle = {{CCA} 2002 Computability and Complexity in Analysis}, editor = {Brattka, Vasco and Schr{\"{o}}der, Matthias and Weihrauch, Klaus}, year = {2002}, series = {Electronic Notes in Theoretical Computer Science}, volume = {66}, publisher = {Elsevier}, address = {Amsterdam}, note = {5th International Workshop, CCA 2002, M{\'{a}}laga, Spain, July 12--13, 2002} } @InProceedings{DHNS03, author = {Downey, Rod G. and Hirschfeldt, Denis R. and Nies, Andr{\'{e}} and Stephan, Frank}, title = {Trivial Reals}, booktitle = {Proceedings of the 7th and 8th Asian Logic Conferences}, editor = {Downey, Rod and Decheng, Ding and Ping, Tung Shih and Hui, Qiu Yu and Yasugi, Mariko}, year = {2003}, pages = {63--102}, publisher = {World Scientific}, address = {Singapore}, note = {7th Conference: Hsi-Tou, Taiwan, June 6--10, 1999; 8th Conference: Chongqing, China, August 29 -- September 2, 2002} } @InCollection{DK79, author = {Demuth, Osvald and Ku{\v{c}}era, A.}, title = {Remarks on constructive mathematical analysis}, booktitle = {Logic Colloquium '78 (Mons, 1978)}, year = {1979}, pages = {81--129}, publisher = {North-Holland}, address = {Amsterdam} } @Article{DK80, author = {Demuth, Osvald and Km{\'\i}nek, V.}, title = {Properties of indefinite constructive {L}ebesgue-{S}tieltjes integrals ({R}ussian)}, journal = {Commentationes Mathematicae Universitatis Carolinae}, year = {1980}, volume = {21}, number = {4}, pages = {629--644} } @Article{DK85, author = {Downey, Rod and Kalantari, Iraj}, title = {Effective extensions of linear forms on a recursive vector space over a recursive field}, journal = {Zeitschrift f\"ur Mathematische Logik und Grundlagen der Mathematik}, year = {1985}, volume = {31}, number = {3}, pages = {193--200} } @Article{DK87, author = {Demuth, Osvald and Ku{\v{c}}era, A.}, title = {Remarks on $1$-genericity, semigenericity and related concepts}, journal = {Commentationes Mathematicae Universitatis Carolinae}, year = {1987}, volume = {28}, number = {1}, pages = {85--94} } @Article{DK89, author = {Du, D. and Ko, Ker-I}, title = {Computational complexity of integration and differentiation of convex functions}, journal = {System Sci.\ and Math.\ Sci.}, year = {1989}, volume = {2}, pages = {70--79} } @Article{DK92, author = {Du, D. and Ko, Ker-I}, title = {A note on best fractions of a computable real number}, journal = {Journal of Complexity}, year = {1992}, volume = {8}, pages = {216--229} } @Article{DKK78, author = {Demuth, Osvald and Kryl, R. and Ku{\v{c}}era, A.}, title = {The use of the theory of functions that are partial recursive relative to numerical sets in constructive mathematics ({R}ussian)}, journal = {Acta Universitatis Carolinae. Mathematica et Physica}, year = {1978}, volume = {19}, number = {1}, pages = {15--60} } @Article{DL02, author = {Downey, Rodney G. and LaForte, Geoffrey L.}, title = {Presentations of computably enumerable reals}, journal = {Theoretical Computer Science}, year = {2002}, volume = {284}, number = {2}, pages = {539--555} } @Article{DMR06, author = {Downey, Rodney and Merkle, Wolfgang and Reimann, Jan}, title = {Schnorr dimension}, journal = {Mathematical Structures in Computer Science}, year = {2006}, volume = {16}, number = {5}, pages = {789--811} } @Article{DN73, author = {Demuth, Osvald and Neme{\v{c}}kova, L.}, title = {The constructive analogue of the property $({T}\sb{1})$ ({R}ussian)}, journal = {Comment. Math. Univ. Carolinae}, year = {1973}, volume = {14}, pages = {421--439} } @InProceedings{DP01, author = {Dunlop, Anthony J. and Pour-El, Marian Boykan}, title = {The Degree of Unsolvability of a Real Number}, booktitle = {Computability and Complexity in Analysis}, editor = {Blanck, Jens and Brattka, Vasco and Hertling, Peter}, year = {2001}, series = {Lecture Notes in Computer Science}, volume = {2064}, pages = {16--29}, publisher = {Springer}, address = {Berlin}, note = {4th International Workshop, CCA 2000, Swansea, UK, September 2000} } @Article{DP79, author = {Demuth, Osvald and Polivka, {\u{I}}.}, title = {The representation of linear functionals in the space of codes of constructive functions that are uniformly continuous on the segment $0\triangle 1$ ({R}ussian)}, journal = {Commentationes Mathematicae Universitatis Carolinae}, year = {1979}, volume = {20}, number = {4}, pages = {765--780} } @InProceedings{DSW86, author = {Dettki, H.J. and Schuster, H. and Weihrauch, K.}, title = {Type 2 recursion theory}, booktitle = {Algebra, Combinatorics and Logic in Computer Science, Vol. 1}, editor = {Demetrovics, J. and Katona, G. and Salomaa, A.}, year = {1986}, series = {Coll. Math. Soc. J\'{a}nos Bolyai}, volume = {42}, pages = {355--361}, note = {Papers from Colloq., Sept. 12--16, 1983, Gy\"or} } @Article{DT02, author = {Downey, Rod and Terwijn, Sebastiaan}, title = {Computably Enumerable Reals and Uniformly Presentable Ideals}, journal = {Mathematical Logic Quarterly}, year = {2002}, volume = {48}, number = {Suppl. 1}, pages = {29--40} } @InProceedings{DWW07, author = {Ding, Decheng and Weihrauch, Klaus and Wu, Yongcheng}, title = {Absolutely non-effective predicates and functions in Computable Analysis}, booktitle = {Theory and Applications of Models of Computation}, editor = {Cai, Jin-Yi and Cooper, S. Barry and Zhou, Hong}, year = {2007}, series = {Lecture Notes in Computer Science}, volume = {4484}, pages = {595--604} } @Article{DWZ04, author = {Downey, Rod and Wu, Guohua and Zheng, Xizhong}, title = {Degrees of d.c.e. reals}, journal = {Mathematical Logic Quarterly}, year = {2004}, volume = {50}, number = {4,5}, pages = {345--350} } @Article{Dah04, author = {Dahlgren, Fredrik}, title = {Computability and continuity in metric partial algebras equipped with computability structures}, journal = {Mathematical Logic Quarterly}, year = {2004}, volume = {50}, number = {4,5}, pages = {486--500} } @InProceedings{Dah06, author = {Dahlgren, Fredrik}, title = {Partial Continuous Functions and Admissible Domain Representations}, booktitle = {Logical Approaches to Computational Barriers}, editor = {Beckmann, A. and Berger, U. and L{\"o}we, B. and Tucker, J.V.}, year = {2006}, series = {Lecture Notes in Computer Science}, volume = {3988}, pages = {94--104}, publisher = {Springer}, address = {Berlin}, note = {Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006} } @Article{Dal05, author = {van Dalen, Dirk}, title = {How the Mathematical Objects Determine the Mathematical Principles}, journal = {Journal of Universal Computer Science}, year = {2005}, volume = {11}, number = {12}, pages = {2132--2141} } @InProceedings{Dal73, author = {van Dalen, Dirk}, title = {Lectures on Intuitionism}, booktitle = {Cambridge Summer School in Mathematical Logic}, editor = {Mathais, A. R. D. and Rogers, H.}, year = {1973}, series = {Lecture Notes in Mathematics}, pages = {1--94}, note = {Aug. 1--21, 1971} } @Article{Dal78, author = {van Dalen, D.}, title = {An interpretation of intuitionistic analysis}, journal = {Ann. Math. Logic}, year = {1978}, volume = {13}, pages = {1--43}, note = {with an appendix by {T}roelstra, A.S.} } @PhdThesis{Dei84a, author = {Deil, Thomas}, title = {Darstellungen und {B}erechenbarkeit reeller {Z}ahlen}, year = {1984}, school = {Fachbereich Mathematik und Informatik}, address = {FernUniversit\"{a}t Hagen} } @Article{Dem65, author = {Demuth, Osvald}, title = {On {L}ebesgue integration in constructive analysis ({R}ussian)}, journal = {Dokl. Akad. Nauk SSSR}, year = {1965}, volume = {160}, pages = {1239--1241} } @Article{Dem67, author = {Demuth, Osvald}, title = {The {L}ebesgue integral in constructive analysis ({R}ussian)}, journal = {Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov.}, year = {1967}, volume = {4}, pages = {30--43}, note = {[translation in: A.O. Slisenko (ed.), Studies in constructive mathematics and mathematical logic, Part II, Consultants Bureau, New York, 1970]} } @Article{Dem67a, author = {Demuth, Osvald}, title = {A necessary and sufficient condition for the {R}iemann integrability of constructive functions}, journal = {Dokl. Akad. Nauk SSSR}, year = {1967}, volume = {176}, pages = {757--758} } @Article{Dem68, author = {Demuth, Osvald}, title = {Fubini's theorem for the {R}iemann integral in constructive mathematics. ({R}ussian)}, journal = {Comment. Math. Univ. Carolinae}, year = {1968}, volume = {9}, pages = {677--686} } @Article{Dem68a, author = {Demuth, Osvald}, title = {The {L}ebesgue integral and the concept of measurability of functions in constructive analysis ({R}ussian)}, journal = {Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov.}, year = {1968}, volume = {8}, pages = {21--28}, note = {[translation in: A.O. Slisenko (ed.), Studies in constructive mathematics and mathematical logic, Part II, Consultants Bureau, New York, 1970]} } @Article{Dem68b, author = {Demuth, Osvald}, title = {The connection between {R}iemann and {L}ebesgue integrability of constructive functions ({R}ussian)}, journal = {Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov.}, year = {1968}, volume = {8}, pages = {29--31}, note = {[translation in: A.O. Slisenko (ed.), Studies in constructive mathematics and mathematical logic, Part II, Consultants Bureau, New York, 1970]} } @Article{Dem69, author = {Demuth, Osvald}, title = {Note on the paper: ``{F}ubini's theorem for the {R}iemann integral in constructive mathematics'' ({R}ussian)}, journal = {Comment. Math. Univ. Carolinae}, year = {1969}, volume = {10}, pages = {115--120} } @Article{Dem69a, author = {Demuth, Osvald}, title = {The differentiability of constructive functions ({R}ussian)}, journal = {Comment. Math. Univ. Carolinae}, year = {1969}, volume = {10}, pages = {167--175} } @Article{Dem69b, author = {Demuth, Osvald}, title = {The spaces ${L}\sb{n}$ and ${S}$ in constructive mathematics ({R}ussian)}, journal = {Comment. Math. Univ. Carolinae}, year = {1969}, volume = {10}, pages = {261--284} } @Article{Dem69c, author = {Demuth, Osvald}, title = {Linear functionals in the constructive spaces ${L}\sb{r}$ ({R}ussian)}, journal = {Comment. Math. Univ. Carolinae}, year = {1969}, volume = {10}, pages = {357--390} } @Article{Dem69d, author = {Demuth, Osvald}, title = {The representability of constructive functions of weakly bounded variation ({R}ussian)}, journal = {Comment. Math. Univ. Carolinae}, year = {1970}, volume = {11}, pages = {421--434} } @Article{Dem69e, author = {Demuth, Osvald}, title = {The {L}ebesgue measurability of sets in constructive mathematic ({R}ussian)}, journal = {Comment. Math. Univ. Carolinae}, year = {1969}, volume = {10}, pages = {463--492} } @Article{Dem70, author = {Demuth, Osvald}, title = {Mean value theorems for the constructive {L}ebesgue integral ({R}ussian)}, journal = {Comment. Math. Univ. Carolinae}, year = {1970}, volume = {11}, pages = {249--269} } @Article{Dem70a, author = {Demuth, Osvald}, title = {The representability of constructive functions of weakly bounded variation ({R}ussian)}, journal = {Comment. Math. Univ. Carolinae}, year = {1970}, volume = {11}, pages = {421--434} } @Article{Dem70b, author = {Demuth, Osvald}, title = {The integrability of derivatives of constructive functions ({R}ussian)}, journal = {Comment. Math. Univ. Carolinae}, year = {1970}, volume = {11}, pages = {667--691} } @Article{Dem70c, author = {Demuth, Osvald}, title = {Necessary and sufficient conditions for the absolute continuity of constructive functions ({R}ussian)}, journal = {Comment. Math. Univ. C