Issue No.03 - March (1968 vol.17)
Abstract?Finding simple or "canonical representations" for regular events is one of the important problems concerning finite automata. The present paper is an attempt to find concatenative canonical decompositions for regular events. Five different decomposition types of regular events are defined, imustrated by examples, and their properties investigated. The main tool in our investigations is the notion of a decomposition set; it is a generalization of the notion of a decomposition state, introduced by the authors in a previous paper.<sup></sup>Let A =(S, M, s<inf>0</inf>, F) be a finite automaton; a subset S??S is a decomposition set if A goes through a state of S? whenever it accepts a tape. In order to determine whether a given subset S??S is a decomposition set one has to check only tapes whose length is not greater than |S|-|S?|-1, where |S| and |S?| are the number of states in S and S?, respectively. Thus, one can deternine all decomposition sets of A. The knowledge of the decomposition sets of A enables one to determine whether and in what form T(A), the set of tapes accepted by A, is decomposable.
Index terms?Canonical expansion, concatenative decomposition, decomposition set, decomposition state, finite automation, prefix (suffix) property, prime event, regular event, right (left) determinate, star event, unambiguous.
A. Paz, "On Concatenative Decompositions of Regular Events", IEEE Transactions on Computers, vol.17, no. 3, pp. 229-237, March 1968, doi:10.1109/TC.1968.229096