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Nonuniform lower bounds for exponential time classes

  • Steven Homer
  • Sarah Mocas
Contributed Papers Structural Complexity Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 969)

Abstract

Lower bounds for the first levels of the exponential time hierarchy with respect to circuit and advice classes are studied. Using time bounded Kolmogorov complexity, languages are constructed which witness that various exponential time classes are not included in (fixed) polynomial advice classes. We show as well that these languages are not included in small circuit families where the circuits are of a fixed, polynomial size. The results yield optimal bounds (up to relativization) on efficient nonuniform computation.

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References

  1. [BDG88]
    J. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity, volume I. Springer-Verlag, New York, 1988.Google Scholar
  2. [BDG90]
    J. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity, volume II. Springer-Verlag, New York, 1990.Google Scholar
  3. [BFNW91]
    L. Babai, L. Fortnow, N. Nisan, and A. Wigderson. BPP has subexponential time simulations unless EXPTIME has publishable proofs. In Proc. 6th IEEE Structure in Complexity Theory, pages 213–219, 1991.Google Scholar
  4. [BH92]
    H. Buhrman and S. Homer. Superpolynomial circuits, almost sparse oracles and the exponential hierarchy. In Proc. of the Conf. on Foundations of Software Technology and Theoretical Computer Science, 1992.Google Scholar
  5. [DT90]
    J. Díaz and J. Torán. Classes of bounded nondeterminism. Math. Systems Theory, 23:21–32, 1990.Google Scholar
  6. [Fu93]
    B. Fu. With quasi-linear queries, EXP is not polynomial time Turing reducible to sparse sets. In Proc. IEEE Structure in Complexity Theory, pages 185–191, 1993.Google Scholar
  7. [GW91]
    R. Gavaldà and O. Watanabe. On the computational complexity of small descriptions. In Proc. 6th IEEE Structure in Complexity Theory, pages 89–101, 1991.Google Scholar
  8. [Hem87]
    L. Hemachandra. Counting in structural complexity theory. Ph.D. Thesis, Cornell University, 1987.Google Scholar
  9. [Hart83]
    J. Hartmanis. Generalized Kolmogorov complexity and the structure of feasible computations. In Proc.24th Annual FOCS Conference, pages 439–445, 1983.Google Scholar
  10. [Kan82]
    R. Kannan. Circuit-size lower bounds and non-reducibility to sparse sets. Information and Control, 55:40–46, 1982.CrossRefGoogle Scholar
  11. [KF80]
    C. M. R. Kintala and P. C. Fischer. Refining nondeterminism in relativized polynomial-time bounded computations. SIAM Journal on Computing, 9:46–53, 1980.Google Scholar
  12. [KL80]
    R. Karp and R. Lipton. Some connections between nonuniform and uniform complexity classes. In Proc. 12th ACM Symposium on Theory of Computing, pages 302–309, 1980.Google Scholar
  13. [L92]
    J. H. Lutz. Almost everywhere high nonuniform complexity. Journal of Computer and System Sciences, pages 220–258, 1992.Google Scholar
  14. [L92a]
    J. H. Lutz. One-way functions and balanced NP. Unpublished manuscript.Google Scholar
  15. [LM93]
    J. H. Lutz and E. Mayordomo. Measure, stochasticity, and the density of hard languages. SIAM Journal on Computing, to appear.Google Scholar
  16. [M93]
    S. E. Mocas. Separating exponential time classes from polynomial time classes. Ph.D. Thesis, Northeastern University, 1993.Google Scholar
  17. [PY93]
    C. H. Papadimitriou and M. Yannakakis. On limited nondeterminism and the complexity of the v-c dimension. In Proc. 8th IEEE Structure in Complexity Theory, pages 12–18, 1993.Google Scholar
  18. [Sch85]
    U. Schöning. Complexity and Structure, volume 211 of Lecture Notes in Computer Science. Springer-Verlag, New York, 1985.Google Scholar
  19. [Wil85]
    C. B. Wilson. Relativized circuit complexity. Journal Computer Systems Sci., 31:169–181, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Steven Homer
    • 1
  • Sarah Mocas
    • 2
  1. 1.Computer Science DepartmentBoston UniversityBoston
  2. 2.Computer Science DepartmentPortland State UniversityPortland

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