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This paper studies decompositions of regular events into star events, i.e. events of the form W = V*. Mathematically, the structure of a star event is that of a monoid. First it is shown that every regular event contains a finite number of maximal star events, which are shown to be regular and can be effectively computed. Necessary and sufficient conditions for a regular event to be the union of its...
This paper presents some results concerning the star height of regular events. First we consider the behavior of star height under various operations on regular events and it is proved that star height is preserved under the derivative operation. The relation of star height of a regular event to the cycle rank of the reduced state graph of the corresponding finite automaton is studied. This investigation...
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