Exact Transversal Hypergraphs and Application to Boolean µ-Functions

Exact Transversal Hypergraphs and Application to Boolean μ-Functions

Application of an Exact Transversal Hypergraph in Selection of SM-Components

The paper deals with the application of the hypergraph theory in selection of State Machine Components (SM-Components) of Petri nets [1,2].As it is known, Petri nets are widely used for modeling of concurrency processes. However, in order to implement the concurrent automaton, an initial Petri net ought to be decomposed into sequential automata (SM-Components), which can be easily designed as a...

Identifying the Minimal Transversals of a Hypergraph and Related Problems

The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. Hypergraph saturation, i.e., given a hypergraph H, decide if every subset of vertices is contained in or contains some edge of H, is shown to be co-NP-complete. A certain subproble...

Irreducible Boolean Functions

This paper is a contribution to the study of a quasi-order on the set Ω of Boolean functions, the simple minor quasi-order. We look at the join-irreducible members of the resulting poset˜Ω. Using a two-way correspondence between Boolean functions and hypergraphs, join-irreducibility translates into a combinatorial property of hypergraphs. We observe that among Steiner systems, those which yield...

Combinatorial Results on Directed Hypergraphs for the SAT Problem

Directed hypergraphs have already been shown to unveil several combinatorial inspired results for the SAT problem. In this paper we approach the SAT problem by searching a transversal of the directed hypergraphs associated to its instance. We introduce some particular clause orderings and study their influence on the backtrack process, exhibiting a new subclass of CNF for which SAT is polynomia...