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...

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Bibliographic Details
Published in:Information processing letters Vol. 74; no. 3; pp. 157 - 162
Main Authors: Kavvadias, Dimitris J., Sideri, Martha, Stavropoulos, Elias C.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 31.05.2000
Elsevier Sequoia S.A
Subjects:
Algorithms
Boolean
Computational complexity
Computer programming
Graphs
Maximal model generation
Output-polynomial
Studies
Transversal hypergraph
Output-polynomial
Transversal hypergraph
Algorithms
Computational complexity
Maximal model generation
ISSN:0020-0190, 1872-6119
Online Access:Get full text
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Summary: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 output-polynomial 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.
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ISSN:0020-0190
1872-6119
DOI:10.1016/S0020-0190(00)00023-5