The Algorithmic Complexity of Modular Decomposition
Modular decomposition is a thoroughly investigated topic in many areas such as switching theory, reliability theory, game theory and graph theory. We propose an O(mn)-algorithm for the recognition of a modular set of a monotone Boolean function f with m prime implicants and n variables. Using this result we show that the computation of the modular closure of a set can be done in time O(mn2). On the other hand, we prove that the recognition problem for general Boolean func tions is NP-complete. Moreover, we introduce the so called generalized Shannon decomposition of a Boolean functions as an efficient tool for proving theorems on Boolean function decompositions.
|Keywords||Boolean functions, computational complexity, decomposition algorithm, modular decomposition, substitution decomposition|
|Publisher||Erasmus Research Institute of Management (ERIM)|
Bioch, J.C.. (2001). The Algorithmic Complexity of Modular Decomposition (No. ERS-2001-30-LIS). Erasmus Research Institute of Management (ERIM). Retrieved from http://hdl.handle.net/1765/99