Journal ArticleDOI
Isomorphism Groups of Automata
Reads0
Chats0
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
More filters
Journal ArticleDOI
Reductive Enumeration Under Mutually Orthogonal Group Actions
TL;DR: In this paper, the authors deal with orbit enumeration within the framework of Burnside's Lemma in a special situation when the group possesses two "mutually orthogonal" actions with respect to fixed points of its elements.
Proceedings ArticleDOI
Automorphism groups and quotients of strongly connected automata and monadic algebras
TL;DR: Applications to decomposition theory, in particular to the problem of factoring out identical parallel front components, are given and a generalization of the major parts of the theory to infinite strongly connected monadic algebras is obtained.
Journal ArticleDOI
Groups of Automorphisms and Sets of Equivalence Classes of Input for Automata
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.
Journal ArticleDOI
Algebraic structures of automata
TL;DR: Among the classes of automata, the class of single bottom automata is considered, and the composition of a single loop automaton and a strongly connected automaton together with its automorphism group is provided.
References
More filters
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.