文章基本信息

标题：The Minimum Oracle Circuit Size Problem
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作者：Eric Allender ; Dhiraj Holden ; Valentine Kabanets 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2015
卷号：30
页码：21-33
DOI：10.4230/LIPIcs.STACS.2015.21
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We consider variants of the Minimum Circuit Size Problem MCSP, where the goal is to minimize the size of oracle circuits computing a given function. When the oracle is QBF, the resulting problem MCSP^QBF is known to be complete for PSPACE under ZPP reductions. We show that it is not complete under logspace reductions, and indeed it is not even hard for TC under uniform AC^0 reductions. We obtain a variety of consequences that follow if oracle versions of MCSP are hard for various complexity classes under different types of reductions. We also prove analogous results for the problem of determining the resource-bounded Kolmogorov complexity of strings, for certain types of Kolmogorov complexity measures.
关键词：Kolmogorov complexity; minimum circuit size problem; PSPACE; NP-intermediate sets