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Functional interpretations of feasibly constructive arithmetic

Published: 01 February 1989 Publication History
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    References

    [1]
    Errctt Bishop. M~thematics as a numerical langllage, in J. Myhill A. Kino and R.E. Ves}cy, e(litors, Inluilionism and Proof Theory: Proceedivgs of the Summer Cov ferencc at BTtffalo, New York, 1968, pages 53--71. North-Holland, Amsterdam, 1970.
    [2]
    Samuel R. Buss. Bounded Arithmetic. Ph.D. dissertation, Princeton University 1985; reprinted Bibliopolis, Nap}es, 1q86. Page references are to the reprinting.
    [3]
    Samuel R. Buss. The polynomial hierarchy and intuitionistic bounded arithmetic, 1986. Structure in Complexity Theory, Springer-Verlag Lecture Notes in Computer Science No. 223, pp. 77-103.
    [4]
    Peter Clote and Gaisi Takeuti. Exponential time and bounded arithmetic, 1986. Structure in Comple~city Theory, Springer-Verlag Lecture Notes in Computer Science No. 223, pp. 125-143.
    [5]
    Alan Cobham. The intrinsic computational difficulty of functions. In Proc. of the 1964 International Congress for Logic, Methodology, and the Philosophy of Sciences, pages 24-30, 1964.
    [6]
    Stephen Cook and Alasdair Urquhart. Functional Interpretations of Feasibly Constructive Arithmetic. Technical Report 210/88, University of Toronto, 1988.
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    Stephen A. Cook. Feasibly constructive proofs and the propositional calculus. In Proc. 7lh A.C.M. Symposium on the Theory of Computation, pages 83-97, 1975.
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    Stephen A. Cook ~nd Robert A. Reckhow. The relative ej~ciency of propositional proof systems. J. Symbolic Logic, 44(1):36-50, March 1979.
    [9]
    Kurt GSdel. 0ber eine bisher noch nicht beniitzte erweiterung des finiten standpunktes. Dialectica 12, 280-287. English translation: j. of Philosophical Logic 9 (1980), 133-142. Revised and expanded English translation to appear ill Volume II of GSdel's Collected Works.
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    A. Haken. The intractability of resolution. Theoretical Computer Science, 39:297-308, 1985.
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    A.S. Troelstra. MetamathematicM investigation of intuitionistic arithmetic and analysis, 1973. Springer-Verlag Lecture Notes in Mathematics, No. 344.

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    cover image ACM Conferences
    STOC '89: Proceedings of the twenty-first annual ACM symposium on Theory of computing
    February 1989
    600 pages
    ISBN:0897913078
    DOI:10.1145/73007
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    Published: 01 February 1989

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    May 14 - 17, 1989
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    • (2022)Models of Bounded Arithmetic Theories and Some Related Complexity QuestionsBulletin of the Section of Logic10.18778/0138-0680.2022.0351:2(163-176)Online publication date: 7-Jun-2022
    • (2016)From positive and intuitionistic bounded arithmetic to monotone proof complexityProceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/2933575.2934570(126-135)Online publication date: 5-Jul-2016
    • (2015)Algebras and coalgebras in the light affine Lambda calculusACM SIGPLAN Notices10.1145/2858949.278475950:9(114-126)Online publication date: 29-Aug-2015
    • (2015)Algebras and coalgebras in the light affine Lambda calculusProceedings of the 20th ACM SIGPLAN International Conference on Functional Programming10.1145/2784731.2784759(114-126)Online publication date: 29-Aug-2015
    • (2010)Feasible functions over co-inductive dataProceedings of the 17th international conference on Logic, language, information and computation10.5555/1886790.1886806(191-203)Online publication date: 6-Jul-2010
    • (2010)Feasible Functions over Co-inductive DataLogic, Language, Information and Computation10.1007/978-3-642-13824-9_16(191-203)Online publication date: 2010
    • (2005)Expressing computational complexity in constructive type theoryLogic and Computational Complexity10.1007/3-540-60178-3_82(131-144)Online publication date: 31-May-2005
    • (2004)Asymptotic Behaviors of Type-2 Algorithms and Induced Baire TopologiesExploring New Frontiers of Theoretical Informatics10.1007/1-4020-8141-3_36(465-478)Online publication date: 2004
    • (2001)On characterizations of the basic feasible functionals, Part IJournal of Functional Programming10.1017/S095679680000384111:1(117-153)Online publication date: 1-Jan-2001
    • (1997)Semantics vs Syntax vs ComputationsJournal of Computer and System Sciences10.1006/jcss.1997.148754:3(424-436)Online publication date: 1-Jun-1997
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