Products of semigroups and applications on state machines
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Date
2015-06-10
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Journal ISSN
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Publisher
University of M'sila
Abstract
The theory of machines that has developed in last twenty years has had a considerable
in uence, not only on the computer systems, but also biology, biochemestry, etc. So here
we will interest in mathematical theory of various types of machines.
The area of mathematics that is of most use to us is that which is known as Modern (or
abstract) algebra. For a hundred years, algebra has developed in diĀ¤erent directions. The
advent of the theory of machines, has provided us with new motivation for the development
of algebra.
Recently the semigroups and groups has become an intresting area of study, and one of
their operations is semidirect product and wreath product .
What we will be doing is to to apply this operations on state machines, by looking at
various types of machines, their properties, and we will replace a general state machine by
a collection of "algebraically simpler" machines connected up in suitable ways (cascade and
wreath product).
This work is devided into three chapters
First we begin with some elementary material concerning the theory of semigroups and
groups.
In the second chapter we have direct product, semidirect product and wreath product
of semigroups and groups.
The third chapter examines many elementary properties of the state machine, the ways
in which it can be connected together (direct, cascade and wreath product) and the use of
this in decompostion theorem.
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Keywords
Products of semigroups and applications on state machines