NDLI: Dimension, entropy rates, and compression

Content Provider	IEEE Xplore Digital Library
Author	Hitchcock, J.M. Vinodchandran, N.V.
Copyright Year	2004
Description	Author affiliation: Dept. of Comput. Sci., Wyoming Univ., USA (Hitchcock, J.M.)
Abstract	This paper develops 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 /spl Delta//sub 3//sup E/, 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 /spl Delta//sub 3//sup E/ and of Lutz (2003) 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 characterizations of the effective dimensions in terms of Kolmogorov complexity rates at the polynomial-space and higher levels have been established, but in the time-bounded setting no such equivalence is known. We introduce the concept of polynomial-time superranking as an extension of ranking. We show that superranking provides an equivalent definition of polynomial-time dimension. From this superranking characterization we show that polynomial-time Kolmogorov complexity rates give a lower bound on polynomial-time dimension.
Sponsorship	IEEE Comput. Soc. Tech. Committee on Found. of Comput. (TCMF)
Starting Page	174
Ending Page	183
File Size	359530
Page Count	10
File Format	PDF
ISBN	0769521207
ISSN	10930159
DOI	10.1109/CCC.2004.1313835
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2004-06-24
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Entropy Polynomials Circuits Complexity theory Computer science Upper bound Fractals Computational complexity Time measurement
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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