Dimension, Entropy Rates, and Compression

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Dimension, Entropy Rates, and Compression
This paper develops new relationships between resource-bounded dimension, entropy rates, and compression. New tools for calculating dimensions are given and used to improve previous results about circuit-size complexity classes. Approximate counting of SpanP functions is used to prove that the NP-entropy rate is an upper bound for dimension in ∆E 3 , the third level of the exponential-time hierarchy. This general result is applied to simultaneously improve the results of Mayordomo (1994) on the measure on P/poly in ∆E 3 and of Lutz (2000) on the dimension of exponential-size circuit complexity classes in ESPACE. Entropy rates of efficiently rankable sets, sets that are optimally compressible, are studied in conjunction with time-bounded dimension. It is shown that rankable entropy rates give upper bounds for time-bounded dimensions. We use this to improve results of Lutz (1992) about polynomial-size circuit complexity classes from resource-bounded measure to dimension. Exact chara...
John M. Hitchcock, N. V. Vinodchandran
Added 01 Jul 2010
Updated 01 Jul 2010
Type Conference
Year 2004
Where COCO
Authors John M. Hitchcock, N. V. Vinodchandran
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