License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2015.21
URN: urn:nbn:de:0030-drops-49013
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/4901/
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Allender, Eric ; Holden, Dhiraj ; Kabanets, Valentine

The Minimum Oracle Circuit Size Problem

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Abstract

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.

BibTeX - Entry

@InProceedings{allender_et_al:LIPIcs:2015:4901,
  author =	{Eric Allender and Dhiraj Holden and Valentine Kabanets},
  title =	{{The Minimum Oracle Circuit Size Problem}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{21--33},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Ernst W. Mayr and Nicolas Ollinger},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/4901},
  URN =		{urn:nbn:de:0030-drops-49013},
  doi =		{10.4230/LIPIcs.STACS.2015.21},
  annote =	{Keywords: Kolmogorov complexity, minimum circuit size problem, PSPACE, NP-intermediate sets}
}

Keywords: Kolmogorov complexity, minimum circuit size problem, PSPACE, NP-intermediate sets
Collection: 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)
Issue Date: 2015
Date of publication: 26.02.2015

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