### Some more on the equivalent transformation of nondeterministic finite automata. Part II. The "deleting" algorithm

Boris Melnikov

#### Abstract

This paper is a continuation of our following previous papers, where we considered some simple algorithms for combining states of the given nondeterministic finite automaton, the reduction some problems related to the star-height to considering automata, and possible classification
of the states and loops of the given automaton. In this part of the paper, we shall describe an algorithm which deletes the state of a given nondeterministic finite automaton. This algorithm preserves basic properties of automata, i.e. the languages of the given and the obtained automata are the same, and the value of star-height for the obtained automaton is no more than such value for the given automaton. Like Part I, we consider two states having the same values of the state marking functions. Then we could apply the same algorithms, but, generally speaking, in the case of the initial conditions considered in this part, the application of combining algorithm of previous part increases the value of star-height of the automaton under consideration. Then we should apply another algorithm, we consider such algorithm in this part. We call it by deleting algorithm, because it deletes a state; however, we not only delete a state, but sometimes add some edges, inputs and outputs before deleting. We also consider some examples of using the described deleting algorithm.

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