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Monotone Boolean dualization is in co-NP[log2n]

University of Patras, Department of Mathematics, GR-265 00 Patras, Greece; University of Patras, Computer Engineering & Informatics Department, GR-265 00 Patras, Greece
Information Processing Letters (Impact Factor: 0.49). 01/2003; DOI: 10.1016/S0020-0190(02)00346-0
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ABSTRACT In 1996, Fredman and Khachiyan [J. Algorithms 21 (1996) 618–628] presented a remarkable algorithm for the problem of checking the duality of a pair of monotone Boolean expressions in disjunctive normal form. Their algorithm runs in no(logn) time, thus giving evidence that the problem lies in an intermediate class between P and co-NP. In this paper we show that a modified version of their algorithm requires deterministic polynomial time plus O(log2n) nondeterministic guesses, thus placing the problem in the class co-NP[log2n]. Our nondeterministic version has also the advantage of having a simpler analysis than the deterministic one.

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