Algorithms in C
Decomposability of partially defined Boolean functions
Discrete Applied Mathematics - Special volume on partitioning and decomposition in combinatorial optimization
Complexity of identification and dualization of positive Boolean functions
Information and Computation
Graph classes: a survey
Learning by discovering concept hierarchies
Artificial Intelligence
Linear-time modular decomposition and efficient transitive orientation of comparability graphs
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
An algorithm for the modular decomposition of hypergraphs
Journal of Algorithms
Minimum self-dual decompositions of positive dual-minor Boolean functions
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Functional Decomposition with Application to FPGA Synthesis
Functional Decomposition with Application to FPGA Synthesis
A New Linear Algorithm for Modular Decomposition
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
On decomposing Boolean functions via extended cofactoring
Proceedings of the Conference on Design, Automation and Test in Europe
An approximation algorithm for cofactoring-based synthesis
Proceedings of the 21st edition of the great lakes symposium on Great lakes symposium on VLSI
Homogeneity vs. adjacency: generalising some graph decomposition algorithms
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Synthesis of P-circuits for logic restructuring
Integration, the VLSI Journal
Minimization of P-circuits using Boolean relations
Proceedings of the Conference on Design, Automation and Test in Europe
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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(mn^2). On the other hand, we prove that the recognition problem for general Boolean functions is coNP-complete. Moreover, we introduce the so-called generalized Shannon decomposition of a Boolean function as an efficient tool for proving theorems on Boolean function decompositions.