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A task of finding for a given Petri net a set of sequential components being able to represent together the behavior of the net arises often in formal analysis of Petri nets and in applications of Petri net to logical control. Such task can be met in two different variants: obtaining a Petri net cover or a decomposition. Petri net cover supposes that a set of the subnets of given net is selected, and the sequential nets forming a decomposition may have additional places, which do not belong to the decomposed net. The paper discusses difference and relations between two mentioned tasks and their results. [ABSTRACT FROM AUTHOR]

Given the discrete state-space system, the set cover problem is defined as selection of the minimal number of global states to cover all the local states. Commonly known methods base on the matrix reduction, boolean function transformation or heuristics ideas. Most of them are inefficient because of computational/memory complexity or non-optimal results. We propose an application of xt-hypergraphs to compute the solution in case where the discrete system can be represented by an xt-hypergraph. Recognition, as well as computation of exact cover in case of xt-hypergraphs is bounded by a polynomial in the number of local states. Therefore, the whole cover process problem turns out to be polynomial. [ABSTRACT FROM AUTHOR]