Abstract
This paper investigates the statistical properties of resource bounded Kolmogorov-random strings. In an attempt to define random sequences, Martin-Löf has shown that the Kolmogorov-random strings (strings with no short description) possess all the statistical properties of random strings. We look at the statistical properties of resource bounded Kolmogorov-random strings. For space bounds, we show that there is a direct relation between the space bound on the Kolmogorov randomness classes and the space required to check a statistical property. The problem is still open for time bounds. We then relate this notion of random sequences to Yao’s definition of secure pseudo random number generators.
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© 1992 Springer-Verlag Berlin Heidelberg
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Longpré, L. (1992). Resource Bounded Kolmogorov Complexity and Statistical Tests. In: Watanabe, O. (eds) Kolmogorov Complexity and Computational Complexity. EATCS Monographs on Theoretical Computer Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77735-6_5
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DOI: https://doi.org/10.1007/978-3-642-77735-6_5
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