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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A generalized concept of automaton automorphisms
TL;DR: The concept of generalized automorphisms is an application to automata theory of a notion established by Ore, which continues the work of Fleck et al concerning the relationship between the structure of automata and their automorphism groups.
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Tape Sets and Automata
TL;DR: Tape sets and a tape set product are defined, and relationships are found between a table of products of tape sets and elements in the operation-preserving group of a finite automaton.
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On a group-matrix type automaton with output
TL;DR: A new type of representation of a strongly connetted group-matrix type automaton of order n on G with output or an (n, O)automaton with output is introduced.
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On the automorphism groups of periodic automata
TL;DR: It is shown that the group of automorphisms of an automaton of this type can be represented as the direct product of two normal subgroups.
References
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Book
The theory of groups
TL;DR: The theory of normal subgroups and homomorphisms was introduced in this article, along with the theory of $p$-groups regular $p-groups and their relation to abelian groups.
Journal ArticleDOI
Finite automata and their decision problems
Michael O. Rabin,Dana Scott +1 more
TL;DR: Finite automata are considered as instruments for classifying finite tapes as well as generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined.
Journal ArticleDOI
The Structure of an Automaton and Its Operation-Preserving Transformation Group
TL;DR: The main result shows the group of operation-preserving transformations of a strongly connected au tomaton onto itself is isomorphic to a group of subsets of input sequences under a certain operation.
Journal ArticleDOI
Some remarks on abstract machines
TL;DR: The Moore-Mealy machine as discussed by the authors is defined as a nonempty set K (of states), D (of inputs), F (of outputs), and two functions a (the next state) function and X (the output) function.