The Algorithmic Complexity of Modular Decomposition
20 Pages Posted: 26 Aug 2006
Date Written: 14 2001 6,
Modular decomposition is a thoroughly investigated topic inmany areas such as switching theory, reliability theory, game theory andgraph theory. We propose an O(mn)-algorithm for the recognition of amodular set of a monotone Boolean function f with m prime implicantsand n variables. Using this result we show that the computation ofthe modular closure of a set can be done in time O(mn2). On the otherhand, we prove that the recognition problem for general Boolean functions is NP-complete. Moreover, we introduce the so called generalizedShannon decomposition of a Boolean functions as an efficient tool forproving theorems on Boolean function decompositions.
Keywords: Boolean functions, computational complexity, decomposition algorithm, modular decomposition, substitution decomposition
JEL Classification: M, M11, R4, C69
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