Generating all maximal models of a Boolean expression

We examine the computational problem of generating all maximal models of a Boolean expression in CNF. We give a resolution-like method that reduces the unnegated variables of an expression while preserving its set of maximal models. We present an output-polynomial algorithm for the 2CNF case and we show that the problem cannot be solved in outputpolynomial time in the case of Horn expressions, unless P = NP, despite an affinity of this case to the recently subexponentially solved transversal hypergraph problem. The problem is of course trivial for 1-valid and anti-Horn expressions, and open for exclusive-ors; it is NP-hard in all other cases.

• Type: Journal
• Year: 2000
• Where: IPL
• Authors: Dimitris J. Kavvadias, Martha Sideri, Elias C. Stavropoulos
• Keywords: Boolean Expression, Computational Problem, IPL 2000, Maximal Models