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.FSTTCS.2015.236
URN: urn:nbn:de:0030-drops-56613
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5661/
Hitchcock, John M. ;
Pavan, A.
On the NP-Completeness of the Minimum Circuit Size Problem
Abstract
We study the Minimum Circuit Size Problem (MCSP): given the
truth-table of a Boolean function f and a number k, does there
exist a Boolean circuit of size at most k computing f? This is a
fundamental NP problem that is not known to be NP-complete. Previous
work has studied consequences of the NP-completeness of MCSP. We
extend this work and consider whether MCSP may be complete for NP
under more powerful reductions. We also show that NP-completeness of
MCSP allows for amplification of circuit complexity.
We show the following results.
- If MCSP is NP-complete via many-one reductions, the following circuit complexity amplification result holds: If NP cap co-NP requires 2^n^{Omega(1)-size circuits, then E^NP requires 2^Omega(n)-size circuits.
- If MCSP is NP-complete under truth-table reductions, then
EXP neq NP cap SIZE(2^n^epsilon) for some epsilon> 0 and EXP neq ZPP. This result extends to polylog Turing reductions.
BibTeX - Entry
@InProceedings{hitchcock_et_al:LIPIcs:2015:5661,
author = {John M. Hitchcock and A. Pavan},
title = {{On the NP-Completeness of the Minimum Circuit Size Problem}},
booktitle = {35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
pages = {236--245},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-97-2},
ISSN = {1868-8969},
year = {2015},
volume = {45},
editor = {Prahladh Harsha and G. Ramalingam},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2015/5661},
URN = {urn:nbn:de:0030-drops-56613},
doi = {10.4230/LIPIcs.FSTTCS.2015.236},
annote = {Keywords: Minimum Circuit Size, NP-completeness, truth-table reductions, circuit complexity}
}
Keywords: |
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Minimum Circuit Size, NP-completeness, truth-table reductions, circuit complexity |
Collection: |
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35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015) |
Issue Date: |
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2015 |
Date of publication: |
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14.12.2015 |