Measure on P: Robustness of the notion
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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.
KeywordsComplexity Class Measure Zero Density System Numerical Argument Conservative Cover
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