The Algorithmic Complexity of Modular Decomposition

20 Pages Posted: 26 Aug 2006

See all articles by Jan C. Bioch

Jan C. Bioch

Erasmus University Rotterdam (EUR) - Centre for Computers and Law; Erasmus Research Institute of Management (ERIM)

Date Written: 14 2001 6,

Abstract

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

Suggested Citation

Bioch, Jan C., The Algorithmic Complexity of Modular Decomposition (14 2001 6,). Available at SSRN: https://ssrn.com/abstract=370893

Jan C. Bioch (Contact Author)

Erasmus University Rotterdam (EUR) - Centre for Computers and Law ( email )

3000 DR Rotterdam
Netherlands

Erasmus Research Institute of Management (ERIM)

P.O. Box 1738
3000 DR Rotterdam
Netherlands

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