The Nondeterministic Complexity of the Fredman and Khachiyan Algorithm for the Dualization of Monotone DNFs ”

In 1996, Fredman and Khachiyan [Journal of Algorithms, 21:618–628, 1996] presented a remarkable algorithm for the problem of checking the duality of a pair of monotone disjunctive normal forms. Their algorithm runs in no(log n) 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(log n) nondeterministic guesses, thus placing the problem in the class co-NP[log n]. Our version of the algorithm has also the advantage of having a simpler analysis than its deterministic one. 1 University of Patras, Department of Mathematics, GR-265 00 Patras, Greece. E-mail: [email protected] 2 University of Patras, Computer Engineering & Informatics Department, GR-265 00 Patras, Greece. E-mail: [email protected] ∗ Corresponding author. TECHNICAL REPORT No. TR2001/12/03 1 COMPUTER TECHNOLOGY INSTITUTE 2001