Minimalizations of NFA Using the Universal Automaton

In this contribution we shall see how our (algebraic) approach to the so-called universal automaton of a given regular language helps to understand the process of the minimalization of a NFA. The minimality is meant with respect to the number of states. Although it is known that the problem is PSPACE-complete (see [5]) one can propose algorithms of not too high complexities to compute relatively good approximations.