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Measure on P: Robustness of the notion

  • Eric Allender
  • Martin Strauss
Contributed Papers Structural Complexity Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 969)

Abstract

In [AS], we defined a notion of measure on the complexity class P (in the spirit of the work of Lutz [L92] that provides a notion of measure on complexity classes at least as large as E, and the work of Mayordomo [M] that provides a measure on PSPACE). In this paper, we show that several other ways of defining measure in terms of covers and martingales yield precisely the same notion as in [AS]. (Similar “robustness” results have been obtained previously for the notions of measure defined by [L92] and [M], but — for reasons that will become apparent below — different proofs are required in our setting.)

To our surprise, and in contrast to the measures of Lutz [L92] and Mayordomo.

Keywords

Complexity Class Measure Zero Density System Numerical Argument Conservative Cover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [AS]
    E. Allender and M. Strauss, Measure on small complexity classes, with applications for BPP, Proc. 35th FOCS conference, 1994 pp. 807–818.Google Scholar
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    D. Juedes and J. Lutz, The complexity and distribution of hard problems, Proc. 34th FOCS Conference, pp. 177–185, 1993.Google Scholar
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    D. Juedes, J. Lutz and E. Mayordomo, private communication, 1993–94.Google Scholar
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    E. Mayordomo, Contributions to the Study of Resource-Bounded Measure, PhD Thesis, Universitat Politècnica de Catalunya, Barcelona, 1994. See also [M2], in which a preliminary version of the PSPACE measure appears.Google Scholar
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    E. Mayordomo, Measuring in PSPACE, to appear in Proc. International Meeting of Young Computer Scientists '92, Topics in Computer Science series, Gordon and Breach.Google Scholar
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    K. Regan, D. Sivakumar, and J.-Y. Cai. Pseudorandom generators, measure theory, and natural proofs. Technical Report UB-CS-TR 95-02, Computer Science Dept., University at Buffalo, January 1995.Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Eric Allender
    • 1
  • Martin Strauss
    • 2
  1. 1.Department of Computer ScienceRutgers UniversityNew Brunswick
  2. 2.Department of MathematicsRutgers UniversityNew Brunswick

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