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
Representations of commutative asynchronous automata
Jing Tian,Xianzhong Zhao +1 more
TL;DR: It is shown that the endomorphism monoid E([email protected]?B) of automaton [email-protected?]B is a Clifford monoid, which generalizes and extends the representations of strongly connected automata given by Ito (1976).
Journal ArticleDOI
A note on structural inference in systems theory
TL;DR: The problem of discovering those properties of systems that remain invariant under a given type of connection is considered and a solution of this problem is proposed for the parallel and serial connections of automata, due to an application of some appropriately formulated rules of the structural inference.
Journal ArticleDOI
On input semigroups of automata
TL;DR: This work stems from Weeg's [10], who considered a similar problem in the discrete case, and a conjecture of Weeg [10, p. 264] is resolved in the negative.
Proceedings ArticleDOI
On the automorphism group of a reduced automaton
TL;DR: The present purpose is to fill the gap to give an isomorphic representation of G(A/H) for arbitrary A and H of the reduced automaton A/H.
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.