• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.595-604
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• 2004

In this paper We shall give some characterizations for mX＊ derived from the relationships between S(m) and C(m). Also we shall discuss the minimal, maximal, strongly cyclic and minmaxCR-automata. There is an interesting part for the relationship between mX＊ and S(m). That is to say, that mX＊ is minimal has the same meaning as S(m) is strongly cyclic. We shall note that the minimality implies ‘ strongly cyclic’ and ‘strongly cyclic’ implies ‘cyclic’ and ‘cyclic’ implies ‘a MaxCR-automaton’.