The complexity of estimating min-entropy

被引：5
|
作者：
Watson, Thomas [1 ]
机构：
[1] Univ Toronto, Dept Comp Sci, Toronto, ON, Canada
来源：
COMPUTATIONAL COMPLEXITY | 2016年 / 25卷 / 01期
基金：
美国国家科学基金会;
关键词：
Complexity; min-entropy; approximate counting; samplable distributions; ARTHUR-MERLIN GAMES; APPROXIMATE; PSEUDORANDOMNESS; PROOFS;
D O I：
10.1007/s00037-014-0091-2
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
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 Lyngso and Pedersen on hidden Markov models (JCSS 65(3):545-569, 2002).
引用
收藏
页码：153 / 175
页数：23
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