Exact Cover of States in the Discrete State-Space System

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 polynotnial.