NDLI: Compressibility and Resource Bounded Measure

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Longpr, Luc Buhrman, Harry
Copyright Year	2002
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 autoreducible 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 subpolynomial dense set has p-measure 0. This strengthens various results.
Starting Page	876
Ending Page	886
Page Count	11
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539797317123
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	3
Volume Number	31
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2001-01-01
Access Restriction	Subscribed
Subject Keyword	compressibility Kolmogorov complexity resource bounded measure Complexity classes Algorithmic information theory
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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Compressibility and Resource Bounded Measure