On a group-matrix type automaton with output

doi:10.1007/BF01951360

Journal Article•DOI•

On a group-matrix type automaton with output

A. Sengupta¹•Institutions (1)

01 Sep 1986-Acta Mathematica Hungarica (Kluwer Academic Publishers)-Vol. 48, Iss: 3, pp 347-352

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.

Abstract: In this paper some results of [6] are extended for a strongly connected groupmatrix type automaton with output. 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. Using this representation we prove some important results on automorphism groups of a strongly connected (n, G)-automaton with output and also on a strongly connected abelian (n, G)-automaton with output.

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Journal Article•DOI•

Introduction to Mathematical Machine Theory

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Seymour Ginsburg

01 Jun 1982-Mathematics of Computation

131 citations

"On a group-matrix type automaton wi..." refers background in this paper

...This means that A' is regular. (Cf. Lemma 3.1 in [ 5 ].)...
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...[ 5 ]]. Now Theorem 3.2 implies that e($)= =~TJ(x)=$=0(~)....
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...[ 5 ]]. This implies that Z(s, a)=Z'(Q(s), a) where Z' is the output-function of the (n, G(A))automaton....
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Journal Article•DOI•

Isomorphism Groups of Automata

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A. C. Fleck¹•Institutions (1)

Michigan State University¹

01 Oct 1962-Journal of the ACM

TL;DR: 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.

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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 moreread less

58 citations

"On a group-matrix type automaton wi..." refers background in this paper

...Lemma 1 and Theorem 2 proved in [ 4 ] can be easily extended as follows:...
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Journal Article•DOI•

Groups of Automorphisms and Sets of Equivalence Classes of Input for Automata

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Bruce H. Barnes¹•Institutions (1)

Pennsylvania State University¹

01 Oct 1965-Journal of the ACM

TL;DR: An investigation is presented which continues the work of Fleck and Weeg concerning the relationships between the equivalence classes of inputs and the group of automorphisms of a finite automaton and the principal result is that if for each state of a strongly connected automaton there exists a subset of the set of equiwfience classes of the input semigroup which constitute t~ group.

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Abstract: An investigation is presented which continues the work of Fleck and Weeg concerning the relationships between the equivalence classes of inputs and the group of automorphisms of a finite automaton. The principal result is that if for each state of a strongly connected automaton there exists a subset of the set of equiwfience classes of the input semigroup which constitute t~ group, then this group is isomorphic to a group of automorphisms of the automaton. The relationship between subautomata and subgroups of the group of autoraorphisms is also studied.

...read moreread less

16 citations

Journal Article•DOI•

A representation of strongly connected automata and its applications

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Masami Ito¹•Institutions (1)

Kyoto Sangyo University¹

01 Aug 1978-Journal of Computer and System Sciences

TL;DR: Some new results about automorphism groups of strongly connected automata are obtained by making use of a new type of representation of stronglyconnected automata introduced.

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Abstract: A new type Of representation of strongly connected automata is introduced. And some new results about automorphism groups of strongly connected automata are obtained by making use of this representation.

...read moreread less

12 citations

"On a group-matrix type automaton wi..." refers background or methods in this paper

...4 in [6]....
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...In this paper some results of [6] are extended for a strongly connected groupmatrix type automaton with output....
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...The above theorem was proved in [6] only for a (1, G)-automaton without output....
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...Now in order to construct a group-matrix type automaton of order n on G or an (n, G)-automaton we recall some important definitions introduced in [6]....
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Journal Article•DOI•

Some results on the relation between automata and their automorphism groups

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Gustav Feichtinger¹•Institutions (1)

IBM¹

01 Dec 1966-Computing

TL;DR: The structure of automata is investigated using the concept of the automorphism group and the investigations about strongly connected automata are extended to cyclic (Oehmke) and normal automata.

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Abstract: In this paper the structure of automata is investigated using the concept of the automorphism group. The investigations about strongly connected automata are extended to cyclic (Oehmke) and normal automata. The set of states is divided into equivalence classes of strongly connected subsets (SCEC). In the set of all SCEC we explain a partial ordering whose minimal elements are called sourceclasses. If there is only one source-classe, the automaton is called cyclic. If each automorphism maps every SCEC onto itself, then the automaton is said to be normal. We generalize some results ofA. Fleck [1]. In some cases we restrict ourselves to Abelian automata.

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11 citations

On a group-matrix type automaton with output

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"On a group-matrix type automaton wi..." refers background in this paper

"On a group-matrix type automaton wi..." refers background in this paper

"On a group-matrix type automaton wi..." refers background or methods in this paper

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