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)


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.


Complexity Class Measure Zero Density System Numerical Argument Conservative Cover 
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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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