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.
Research supported by NSF grant CCR-9204874.
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References
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Allender, E., Strauss, M. (1995). Measure on P: Robustness of the notion. In: Wiedermann, J., Hájek, P. (eds) Mathematical Foundations of Computer Science 1995. MFCS 1995. Lecture Notes in Computer Science, vol 969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60246-1_119
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DOI: https://doi.org/10.1007/3-540-60246-1_119
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