A stronger Kolmogorov zero-one law for resource-bounded measure

Authors:
Jack Jie Dai
Affiliations:
Mathematics Department, Iowa State University, Ames, IA
Venue:
Theoretical Computer Science - Algorithms,automata, complexity and games
Year:
2003

Citing 3
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Resource-Bounded Measure

COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity

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Abstract

Resource-bounded measure has been defined on the classes E, E2, ESPACE, E2SPACE, REC, and the class of all languages. It is shown here that if C is any of these classes and X is a set of languages that is closed under finite variations and has outer measure 1 in C, then X has measure 0 in C. This result strengthens Lutz's resource-bounded generalization of the classical Kolmogorov zero-one law. It also gives a useful sufficient condition for proving that a set has measure 0 in a complexity class.