• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.585-593
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• 2004

In this paper we shall discuss the minimal, maximal and primary subautomata. Also the concepts of the totally reachable state and source will be introduced. It is an interesting part that mX＊ is minimal iff the source S(m) is maximal. We shall point out that the characterization of primary subautomaton comes from the properties associated with the sources S(m)'s.

• 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’.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.663-670
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• 2005

In this paper we shall give some decompositions derived from cyclic subautomata or neighborhoods of the automaton. Also we shall discuss some characterizations of cyclic automata when an automaton is maximal cyclic refinement. If m $\in$ M is totally reachable state, we shall see that {$mX^{\ast}$} is minimal.