Extended basis finite automaton. Part I. The basic definitions

Boris Melnikov, Aleksandra Melnikova

Abstract


In this paper, we consider a special extension of the class of non-deterministic finite automata. The purpose of this consideration is the following: first, to describe using such automata various brute-force algorithms of equivalent transformation of automata; secondly, the application of the described extension in several minimization problems for ordinary non-deterministic finite automata; thirdly, with the help of these automata we can simplify some proofs, which are also necessary for ordinary finite automata. In the paper, we consider the definition of extended finite automata, give examples, define the extended basic finite automaton for the given regular language and consider some properties of this automaton. We also prove, that for the extended basis automaton all the auxiliary languages obtained in the constructions are regular. All this allows to simplify the definition of an extended basic automaton. We also show the adequacy of the definition of an extended basis finite automaton, i.e. we prove the assertion that the extended basic automaton constructed on the basis of the source regular language really defines this language. And on one of the examples we show the following fact: there are regular languages, in whose basic automata some vertices do not have cycles corresponding to the cycles of the corresponding vertices of other equivalent automata; such cycles exist in similar vertices of extended basic automata.

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References


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