A satisfiability algorithm and average-case hardness for formulas over the full binary basis

We present a moderately exponential time algorithm for the satisfiability of Boolean formulas over the full binary basis. For formulas of size at most cn , our algorithm runs in time for some constant μ c > 0. As a byproduct of the running time analysis of our algorithm, we obtain strong average...

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Bibliographic Details
Published in:	Computational complexity Vol. 22; no. 2; pp. 245 - 274
Main Authors:	Seto, Kazuhisa, Tamaki, Suguru
Format:	Journal Article
Language:	English
Published:	Basel SP Birkhäuser Verlag Basel 01.06.2013
Subjects:	Algorithm Analysis and Problem Complexity Computational Mathematics and Numerical Analysis Computer Science exact algorithm 68Q25 68Q17 average-case hardness formula parity gate Satisfiability
ISSN:	1016-3328, 1420-8954
Online Access:	Get full text
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Summary:	We present a moderately exponential time algorithm for the satisfiability of Boolean formulas over the full binary basis. For formulas of size at most cn , our algorithm runs in time for some constant μ c > 0. As a byproduct of the running time analysis of our algorithm, we obtain strong average-case hardness of affine extractors for linear-sized formulas over the full binary basis.
ISSN:	1016-3328 1420-8954
DOI:	10.1007/s00037-013-0067-7