NDLI: The complexity of estimating min-entropy

Content Provider	Springer Nature Link
Author	Watson, Thomas
Copyright Year	2014
Abstract	Goldreich et al. (CRYPTO 1999) proved that the promise problem for estimating the Shannon entropy of a distribution sampled by a given circuit is NISZK-complete. We consider the analogous problem for estimating the min-entropy and prove that it is SBP-complete, where SBP is the class of promise problems that correspond to approximate counting of NP witnesses. The result holds even when the sampling circuits are restricted to be 3-local. For logarithmic-space samplers, we observe that this problem is NP-complete by a result of Lyngsø and Pedersen on hidden Markov models (JCSS 65(3):545–569, 2002).
Ending Page	175
Page Count	23
Starting Page	153
File Format	PDF
ISSN	10163328
e-ISSN	14208954
Journal	Computational complexity
Issue Number	1
Volume Number	25
Language	English
Publisher	Springer International Publishing
Publisher Date	2014-09-06
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	samplable distributions Computational Mathematics and Numerical Analysis approximate counting min-entropy Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) Algorithm Analysis and Problem Complexity Complexity
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Computational Theory and Mathematics Computational Mathematics

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The complexity of estimating min-entropy