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Compressibility and resource bounded measure

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STACS 96 (STACS 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1046))

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Abstract

We give a new definition of resource bounded measure based on compressibility of infinite binary strings. We prove that the new definition is equivalent to the one commonly used. This new characterization offers us a different way to look at resource bounded measure, shedding more light on the meaning of measure zero results and providing one more tool to prove such results.

The main contribution of the paper is the new definition and the proofs leading to the equivalence result. We then show how this new characterization can be used to prove that the class of linear auto-reducible sets has p-measure 0. We also prove that the class of sets that are truth-table reducible to a p-selective set has p-measure 0 and that the class of sets that Turing reduce to a sub-polynomial dense set has p-measure 0. This strengthens various results.

Partially suported by the Dutch foundation for scientific research (NWO) through NFI Project ALADDIN, under contract number NF 62-376.

Supported in part by NSF Grant CCR-9211174 and NSF Grant INT-9123551.

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Claude Puech Rüdiger Reischuk

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© 1996 Springer-Verlag Berlin Heidelberg

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Buhrman, H., Longpré, L. (1996). Compressibility and resource bounded measure. In: Puech, C., Reischuk, R. (eds) STACS 96. STACS 1996. Lecture Notes in Computer Science, vol 1046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60922-9_2

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  • DOI: https://doi.org/10.1007/3-540-60922-9_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60922-3

  • Online ISBN: 978-3-540-49723-3

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