Baire’s Categories on Small Complexity Classes (original) (raw)

Abstract

We generalize resource-bounded Baire’s categories to small complexity classes such as P, QP and SUBEXP and to probabilistic classes such as BPP. We give an alternative characterization of small sets via resource-bounded Banach-Mazur games. As an application we show that for almost every language A ∈ SUBEXP, in the sense of Baire’s category, P A = BPP A.

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References

  1. Lutz, J.: Category and measure in complexity classes. SIAM Journal on Computing 19, 1100–1131 (1990)
    Article MATH MathSciNet Google Scholar
  2. Lutz, J.: Almost everywhere high nonuniform complexity. Journal of Computer and System Science 44, 220–258 (1992)
    Article MATH MathSciNet Google Scholar
  3. Allender, E., Strauss, M.: Measure on small complexity classes, with application for BPP. In: Proceedings of the 35th Annual IEEE Symposium on Foundations of Computer Science, pp. 807–818 (1994)
    Google Scholar
  4. Strauss, M.: Measure on P-strength of the notion. Inform. and Comp. 136(1), 1–23 (1997)
    Article MATH Google Scholar
  5. Regan, K., Sivakumar, D.: Probabilistic martingales and BPTIME classes. In: Proc. 13th Annual IEEE Conference on Computational Complexity, pp. 186–200 (1998)
    Google Scholar
  6. Moser, P.: A generalization of Lutz’s measure to probabilistic classes (2002) (submitted)
    Google Scholar
  7. Ambos-Spies, K.: Resource-bounded genericity. In: Proceedings of the Tenth Annual Structure in Complexity Theory Conference, pp. 162–181 (1995)
    Google Scholar
  8. Balcázar, J.L., Díaz, J., Gabarró, J.: Structural Complexity I. EATCS Monographs on Theorical Computer Science, vol. 11. Springer, Heidelberg (1995)
    Google Scholar
  9. Balcázar, J.L., Díaz, J., Gabarró, J.: Structural Complexity II. EATCS Monographs on Theorical Computer Science, vol. 22. Springer, Heidelberg (1990)
    Google Scholar
  10. Papadimitriou, C.: Computational complexity. Addison-Wesley, Reading (1994)
    Google Scholar
  11. Klivans, A., Melkebeek, D.: Graph nonisomorphism has subexponential size proofs unless the polynomial hierarchy collapses. In: Proceedings of the 31st Annual ACM Symposium on Theory of Computing, pp. 659–667 (1999)
    Google Scholar
  12. Impagliazzo, R., Widgerson, A.: P = BPP if E requires exponential circuits: derandomizing the XOR lemma. In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing, pp. 220–229 (1997)
    Google Scholar
  13. Moser, P.: Locally computed Baire’s categories on small complexity classes (2002) (submitted)
    Google Scholar

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Authors and Affiliations

  1. Computer Science Department, University of Geneva,
    Philippe Moser

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Editors and Affiliations

  1. Department of Computer Science, Lund University, 22100, Lund, Sweden
    Andrzej Lingas
  2. School of Technology and Society, Malmö University, SE-205 06, Malmö, Sweden
    Bengt J. Nilsson

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Moser, P. (2003). Baire’s Categories on Small Complexity Classes. In: Lingas, A., Nilsson, B.J. (eds) Fundamentals of Computation Theory. FCT 2003. Lecture Notes in Computer Science, vol 2751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45077-1\_31

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