An approach to algorithmizing the problem of vertex minimization of nondeterministic automata. Part I. Problem statement and the brief description of the basis methods

Abstract

We consider our approach to the problem of vertex minimization of nondeterministic finite automata. It comes down to constructing a lot of grids and knocking out on its basis an optimal (or pseudo-optimal) subset. However, our problem is much more complicated than the classical problem of optimal coverage of a set, since we need to succeed (to build pseudo-optimal solutions in an acceptable time) in its particular case; in this particular case, we are considering has many specific features, which are not characteristic of most other variants of the problem of optimal coverage of a set. In the first part of the paper, we consider issues related to the brief description of the basic branch-and-bound method, testing approach to the basic method, and some modifications the basic algorithm.