Some properties of the basis finite automaton

Abstract

The present paper discusses non-deterministic finite Rabin-Scott's automata. The majority of works recently dealing with this subject were, in fact, concerned only with properties of a canonical form automata or of some objects equivalent to it. This article continues the series of works in which the authors state a different point of view, describing the finite automata as just another invariant of the given regular language called basis finite automaton. In this article the authors argue on some new properties for the basis finite automaton. One of them is included into basis automaton's table of binary relations. It is stated that this table can not contain either identical strings or identical columns. Another property depicts a possibility to obtain any finite automaton for a given regular language by the process of duplicating or combining some of its states.