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Some Relations Between Subsystems of Arithmetic and Complexity of Computations

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Logic from Computer Science

Part of the book series: Mathematical Sciences Research Institute Publications ((MSRI,volume 21))

Abstract

We shall introduce a special mode of interactive computations of optimal solutions to optimization problems. A restricted version of such computations was used in [KPT] to show that T i2 = S i+12 implies ∑ p i+2 = П p i+2 . Here we shall reduce the question whether T i2 = S i2 to a question about interactive computations (in a more general sense) of some optimization problems.

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References

  1. S. R. Buss, Bounded Arithmetic, Bibliopolis, Napoli, 1986.

    MATH  Google Scholar 

  2. S. R. Buss , Axiomatizations and conservation results for fragments of bounded arithmetic, Contemporary Mathematics, AMS Proc. of Workshop in Logic and Computation, 1987 106 (1990), 57–84.

    MathSciNet  Google Scholar 

  3. S. R. Buss, The Polynomial Hierarchy and intuitionistic bounded arithmetic, in “Structure in Complexity Theory”, LNCS 223, Springer-Verlag, 1986, pp. 77–103.

    Google Scholar 

  4. S. A. Cook, Feasibly constructive proofs and the propositional calculus, Proc. 7-th STOC (1975), 73–89

    Google Scholar 

  5. J. Krajíček, No counterexample interpretation and interactive computations, these proceedings.

    Google Scholar 

  6. J. Krajíček and P. Pudlák, Quantified propositional calculi and fragments of bounded arithmetic, Zeitschrift f. Math. Logik 36(1) (1990), 29–46.

    Article  MATH  Google Scholar 

  7. J. Krajíček, P. Pudlák and G. Takeuti, Bounded arithmetic and Polynomial Hierarchy, Annals of Pure and Applied Logic, to appear.

    Google Scholar 

  8. J. Krajicek and G. Takeuti, On induction-free provability, Discrete Applied Mathematics (to appear).

    Google Scholar 

  9. G. Kreisel, On the interpretation of non-finitist proofs, JSL 16 (1951), 241–267.

    Article  MathSciNet  MATH  Google Scholar 

  10. J. Paris and A. Wilkie, On the scheme of induction for bounded arithmetic formulas, Annals of Pure and Applied Logic 35(3) (1987), 205–303.

    MathSciNet  Google Scholar 

  11. R. Parikh, Existence and feasibility in arithmetic, JSL 36 (1971), 494–508.

    Article  MathSciNet  MATH  Google Scholar 

  12. P. Pudlak, A note on bounded arithmetic, Fundamenta Mathematicae, to appear.

    Google Scholar 

  13. H. Schwichtenberg, Proof Theory: Some applications of cut-elimination, in “Handbook of Mathematical Logic”, J. Barwise ed. (1977), 867–895.

    Chapter  Google Scholar 

  14. G. Takeuti, Some relations among systems of bounded arithmetic, Preprint.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Mathematical Institue ČSAV, Žitná 25, Praha 1, Czechoslovakia

    Pavel Pudlák

  2. Mathematical Science Research Institute, Berkeley, CA, 94720, USA

    Pavel Pudlák

Authors
  1. Pavel Pudlák
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California at Los Angeles, 90024-1766, Los Angeles, CA, USA

    Yiannis N. Moschovakis

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© 1992 Springer-Verlag New York, Inc

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Pudlák, P. (1992). Some Relations Between Subsystems of Arithmetic and Complexity of Computations. In: Moschovakis, Y.N. (eds) Logic from Computer Science. Mathematical Sciences Research Institute Publications, vol 21. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2822-6_19

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  • DOI: https://doi.org/10.1007/978-1-4612-2822-6_19

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7685-2

  • Online ISBN: 978-1-4612-2822-6

  • eBook Packages: Springer Book Archive

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