Skip to main content
Springer Nature Link
Log in

Relations Between Average-Case and Worst-Case Complexity

  • Conference paper
Fundamentals of Computation Theory (FCT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3623))

Included in the following conference series:

  • 895 Accesses

Abstract

The consequences of the worst-case assumption NP = P are very well understood. On the other hand, we only know a few consequences of the average-case assumption “NP is easy on average.” In this paper we establish several new results on the worst-case complexity of Arthur-Merlin games (the class AM) under the average-case complexity assumption “NP is easy on average.”

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Arvind, V., Köbler, J.: New lowness results for ZPPNP. Journal of Computer and System Sciences 65(2), 257–277 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. Babai, L.: Trading group theory for randomness. In: Proc. 17th Annual ACM Symp. on Theory of Computing, pp. 421–429 (1985)

    Google Scholar 

  3. Ben-David, S., Chor, B., Goldreich, O., Luby, M.: On the theory of average case complexity. Journal of Computer and System Sciences 44(2), 193–219 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  4. Balcázar, J., Diaz, J., Gabarró, J.: Structural Complexity I. Springer, Berlin (1988)

    MATH  Google Scholar 

  5. Babai, L., Fortnow, L., Nisan, N., Wigderson, A.: BPP has subexponential time simulations unless exptime has publishable proofs. In: Proceedings of the 6th Annual Conference on Structure in Complexity Theory, 1991, pp. 213–219 (1991)

    Google Scholar 

  6. Buhrman, H., Fortnow, L., Pavan, A.: Some results on derandomization. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 212–222. Springer, Heidelberg (2003)

    Google Scholar 

  7. Babai, L., Moran, S.: Arthur-merlin games: a randomized proof system, and a hierarchy of complexity class. Journal of Computer and System Sciences 36(2), 254–276 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  8. Buhrman, H.: Resource bounded reductions. PhD thesis, University of Amsterdam (1993)

    Google Scholar 

  9. Feige, U., Lund, C.: On the hardness of computing permanent of random matrices. In: Proceedings of 24th Annual ACM Symposium on Theory of Computing, pp. 643–654 (1992)

    Google Scholar 

  10. Gemmel, P., Sudan, M.: Higly resilient correctors for polynomials. Information Processing Letters 43, 169–174 (1992)

    Article  MathSciNet  Google Scholar 

  11. Gutfreund, D., Shaltiel, R., Ta-Shma, A.: Uniform hardness vs. randomness tradeoffs for Arth ur-Merlin games. Computational Complexity 12, 85–130 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Gurevich, Y.: Average case completeness. Journal of Computer and System Sciences 42, 346–398 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  13. Impagliazzo, R.: A personal view of average-case complexity theory. In: Proceedings of the 10th Annual Conference on Structure in Complexity Theory, pp. 134–147. IEEE Computer Society Press, Los Alamitos (1995)

    Chapter  Google Scholar 

  14. Impagliazzo, R., Wigderson, A.: P = BPP if E requires exponential circuits: Derandomizing the XOR lemma. In: Proceedings of the 29th ACM Symposium on Theory of Computing, pp. 220–229 (1997)

    Google Scholar 

  15. Köbler, J., Schuler, R.: Average-case intractability vs. worst-case intractability. Information and Computation 190(1), 1–17 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  16. Klivans, A., van Melkebeek, D.: Graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses. SIAM Journal on Computing 31, 1501–1526 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  17. Levin, L.: Average case complete problems. SIAM Journal of Computing 15, 285–286 (1986)

    Article  MATH  Google Scholar 

  18. Lipton, R.: New directions in testing. In: Distributed Computing and Cryptography. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 2, pp. 191–202. American Mathematics Society (1991)

    Google Scholar 

  19. Papadimitriou, C.: Computational Complexity. Addison-Wesley, Reading (1994)

    MATH  Google Scholar 

  20. Shaltiel, R., Umans, C.: Simple extractors for all min-entropies and a new pseudo-random generator. In: 42nd IEEE Symposium on Foundations of Computer Science, pp. 648–657 (2001)

    Google Scholar 

  21. Shaltiel, R., Umans, C.: Pseudorandomness for approximate counting and sampling. Technical Report TR 04-086, ECCC (2004)

    Google Scholar 

  22. Valiant, L., Vazirani, V.: NP is as easy as detecting unique solutions. In: Proc. 17th ACM Symp. Theory of Computing, pp. 458–463 (1985)

    Google Scholar 

  23. Žák, S.: A Turing machine time hierarchy. Theor. Computer Science 26, 327–333 (1983)

    Article  MATH  Google Scholar 

  24. Wang, J.: Average-case computational complexity theory. In: Hemaspaandra, L., Selman, A. (eds.) Complexity Theory Retrospective II, pp. 295–328. Springer, Heidelberg (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Iowa State University,  

    A. Pavan

  2. Department of Computer Science and Engineering, University of Nebraska-Lincoln,  

    N. V. Vinodchandran

Authors
  1. A. Pavan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. V. Vinodchandran
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Theoretische Informatik, Universität zu Lübeck, Germany

    Maciej Liśkiewicz

  2. Institut für Theoretische Informatik, Universität zu Lübeck, Ratzeburger Allee 160, 23538, Lübeck, Germany

    Rüdiger Reischuk

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pavan, A., Vinodchandran, N.V. (2005). Relations Between Average-Case and Worst-Case Complexity. In: Liśkiewicz, M., Reischuk, R. (eds) Fundamentals of Computation Theory. FCT 2005. Lecture Notes in Computer Science, vol 3623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537311_37

Download citation

  • DOI: https://doi.org/10.1007/11537311_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28193-1

  • Online ISBN: 978-3-540-31873-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics