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Nondeterministic Instance Complexity and Hard-to-Prove Tautologies

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STACS 2000 (STACS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1770))

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Abstract

In this note we first formalize the notion of hard tautologies using a nondeterministic generalization of instance complexity. We then show, under reasonable complexity-theoretic assumptions, that there are infinitely many propositional tautologies that are hard to prove in any sound propositional proof system.

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References

  1. J. L. Balcázar, J. Díaz, and J. Gabarró, Structural Complexity I, EATCS Monographs on Theoretical Computer Science. Springer-Verlag, second edition, 1995.

    Google Scholar 

  2. P. Beame and T. Pitassi, Propositional proof complexity: past, present, and future, ECCC Report TR98-067, 1998.

    Google Scholar 

  3. H. Buhrman and L. Fortnow, Resource-bounded Kolmogorov complexity revisited, In Proceedings of the 14th Symposium on Theoretical Aspects of Computer Science, LNCS, 1200: 105–116, Springer, 1997.

    Google Scholar 

  4. S. A. Cook and R. A. Reckhow, The relative efficiency of propositional proof systems, Journal of Symbolic Logic, 44(1):36–50, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  5. L. Fortnow and M. Kummer, On resource-bounded instance complexity, Theoretical Computer Science A, 161:123–140, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Kadin, PNP[log n]and sparse Turing-complete sets for NP, Journal of Computer and System Sciences, 39(3):282–298, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  7. P. Orponen, K. Ko, U. Schöning, and O. Watanabe, Instance complexity, Journal of the ACM, 41:96–121, 1994.

    Article  MATH  Google Scholar 

  8. J. Krajícek, Bounded arithmetic, propositional logic, and complexity theory, Cambridge University Press, 1995.

    Google Scholar 

  9. M. Li and P. Vitanyi, Kolmogorov complexity and applications, Springer Verlag, 1993.

    Google Scholar 

  10. N. Lynch, On reducibility to complex or sparse sets, Journal of the ACM, 22:341–345, 1975.

    Article  MATH  MathSciNet  Google Scholar 

  11. M. Mundhenk, NP-hard sets have many hard instances, In Proc. MFCS, LNCS 1295, 428–437, Springer Verlag, 1997.

    Google Scholar 

  12. S. Riis and M. Sitharam, Generating hard tautologies using predicate logic and the symmetric group, BRICS Report RS-98-19.

    Google Scholar 

  13. U. Schöning, Complexity cores and hard to prove formulas, In Proc. CSL, LNCS, Springer Verlag, 273–280, 1987.

    Google Scholar 

  14. M. Sipser, A complexity theoretic approach to randomness, In Proc. ACM STOC, 330–335, 1983.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Mathematical Sciences, C.I.T Campus, Madras, 600113, India

    Vikraman Arvind

  2. Institut für Informatik, Humboldt-Universität zu Berlin, D-10099, Berlin, Germany

    Johannes Köbler

  3. Fachbereich IV — Informatik, Universität Trier, D-54286, Trier, Germany

    Martin Mundhenk

  4. Theoretische Informatik, Universität Ulm, D-89069, Ulm, Germany

    Jacobo Torán

Authors
  1. Vikraman Arvind
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  2. Johannes Köbler
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  3. Martin Mundhenk
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  4. Jacobo Torán
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Dept. of Theoretical Computer Science, Universität Dresden, 01062, Dresden, Germany

    Horst Reichel

  2. Université de Lille, LIFL - UPRESA 8022, CNRS, Bât. M3 - UFR IEEA, 59655, Villeneuve d’ASCQ Cedex, France

    Sophie Tison

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© 2000 Springer-Verlag Berlin Heidelberg

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Arvind, V., Köbler, J., Mundhenk, M., Torán, J. (2000). Nondeterministic Instance Complexity and Hard-to-Prove Tautologies. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_26

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  • DOI: https://doi.org/10.1007/3-540-46541-3_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67141-1

  • Online ISBN: 978-3-540-46541-6

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