Comparing reductions to NP-complete sets
Information and Computation
On the polynomial depth of various sets of random strings
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Comparing reductions to NP-complete sets
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
On the polynomial depth of various sets of random strings
Theoretical Computer Science
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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.