The Algorithmic Complexity of Modular Decomposition

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