Affiliation:
1. University of Waterloo, Department of Applied Analysis and Computer Science, Waterloo, Ontario, Canada
Abstract
Decompositions of regular events into star events, i.e. events of the form
W
=
V
*, are studied. 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.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference8 articles.
1. HARTMANIS J. AND STEARNS R .E . Algebraic Structure Theory of Sequential Machine. Prentice-Hall Englewood Cliffs N. J. 1966. HARTMANIS J. AND STEARNS R .E . Algebraic Structure Theory of Sequential Machine. Prentice-Hall Englewood Cliffs N. J. 1966.
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