8th Annual Symposium on Switching and Automata Theory (SWAT 1967) (1967)
Oct. 18, 1967 to Oct. 20, 1967
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.1967.21
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 maximal star events are found. Next, star events are factored out from arbitrary events, yielding the form W=V*T. For each W there exists a unique largest V* and a unique smallest T; an algorithm for finding suitable regular expressions for V and T is developed. Finally, an open problem of Paz and Peleg is answered: Every regular event is decomposable as a finite product of star events and prime events.
R. Cohen and J. A. Brzozowski, "On decompositions of regular events," 8th Annual Symposium on Switching and Automata Theory (SWAT 1967)(FOCS), Texas, 1967, pp. 255-264.