Journal ArticleDOI
Isomorphism Groups of Automata
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TLDR
For a certain class of automata a necessary and sufficient condition, in terms of the group of the automaton, is given for insuring that an automaton can be represented as a direct product.Abstract:
This paper persues a discussion of certain algebraic properties of automata and their relationship to the structure (i.e., properties of the next state function) of automata. The device which is used for this study is the association of a group with each automaton. We introduce functions on automata and study the group of an automaton, a representation for the group elements and the direct product of automata. Finally, for a certain class of automata a necessary and sufficient condition, in terms of the group of the automaton, is given for insuring that an automaton can be represented as a direct product.read more
Citations
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Journal ArticleDOI
Structure and Transition-Preserving Functions of Finite Automata
TL;DR: Arbitrary finite automata are decomposed into their major substructures, the primaries, and various characterizations of these transition-preserving functions on singly generated Automata are presented and are used as a basis for the reduction.
Journal ArticleDOI
Automorphisms of Polyadic Automata
TL;DR: The results of an investigation of relationships concerning the group of automorphisms, the polyadic group of defined polyadic automata and the structure of thepolyadic automation and the ordinary automata associated and with thePolyadic automaton are presented.
Journal ArticleDOI
On the Automorphism Group of an Automaton
TL;DR: The algebraic properties of automata are investigated and the automorphism group of an automaton and a certain associated semigroup are the devices used in the study.
Journal ArticleDOI
The cartesian composition of automata
TL;DR: This paper introduces a new product called the cartesian composition and discusses how various properties of the product automaton depend on the corresponding properties ofThe factors.
Journal ArticleDOI
Group-Type Automata
TL;DR: The purpose is to investigate the input structure of automata which have a group-like character and the class of perfect automata investigated by Fleck and Weeg is a proper subclass of those considered here.
References
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Proceedings ArticleDOI
Some remarks on abstract machines
TL;DR: Much of the recent literature has dealt with questions almost exclusively of mathematical, as contrasted with engineering, interest, and the present paper is written in that spirit.