Showing papers on "ω-automaton published in 1973"
Journal Article•
16 citations
01 Jan 1973
TL;DR: In this article, it is shown that for any invertible linear finite automaton there exists a linear finite memory automaton as its inverse, and the structure of the family of such inverses is discussed.
Abstract: This paper deals with the invertibility problem for linear finite automata by means of matrix transformation method. It is shown that for any invertible linear finite automaton there exists a linear finite memory automaton as its inverse. Then we discuss the structure of the family of such inverses and give a procedure for synthesizing these inverses and the correspondent invertible finite automata.
16 citations
TL;DR: Each set of all passive, Garden-of-Eden, and branching point state configurations is defined and shown to constitute a regular set, and regularity is proved to hold for the fixed, cyclic, open and reflexive boundary conditions.
10 citations
TL;DR: From this group theoretic characterization of linear permutation automata, a complete characterization of all homomorphisms of a linear automaton which yield linearly realizable image automata is derived as well as several results about the structure of linear automata.
8 citations
TL;DR: The transition probabilities of the stochastic automata introduced in this paper are dependent upon the number of times the current state has been passed by.
Abstract: The transition probabilities of the stochastic automata we introduce in this paper are dependent upon the number of times the current state has been passed by. All the possible ways an automaton can develop, are represented by a set of matrices, which is formally characterized.
8 citations
TL;DR: It is proved that a language is multistochastic if and only if it is a homomorphic image of a stochastic language and for those multistechastic automata in which spontaneous state transitions are not allowed.
Abstract: The notion of a multistochastic automaton is defined. Several language families are obtained and investigated. It is proved that a language is multistochastic if and only if it is a homomorphic image of a stochastic language. The same holds also for λ -free homomorphisms and for those multistochastic automata in which spontaneous state transitions are not allowed. These two results are valid for regular substitutions and λ -free regular substitutions, too. Some closure properties of the considered language families are established. Finally, it is shown that multistochastic automata and stochastic sequential machines are closely related to each other.
7 citations
01 Jan 1973
TL;DR: An alternative proof is presented which reduces the emptiness problem for automata on infinite trees to that for Automata on finite trees, much simpler than Rabin's.
Abstract: : In a previous paper Rabin defined Automata on Infinite Trees, and the body of that paper is concerned with proving two theorems about these automata. The result the author considers in the report states that there exists an effective procedure to determine, given an automaton on infinite trees, whether or not it accepts anything at all. An alternative proof is presented which reduces the emptiness problem for automata on infinite trees to that for automata on finite trees. This proof is much simpler than Rabin's.
5 citations
TL;DR: A certain class of composite binary automata with strongly connected component automata is studied, giving a powerful method to construct automata or generate binary sequences with certain prescribed properties.
Abstract: A certain class of composite binary automata with strongly connected component automata is studied. Features as equivalence, reduction, and minimality of automata are considered. All quantities are expressed by simple properties of the component automata and the connecting network. This gives a powerful method to construct automata or generate binary sequences with certain prescribed properties.
4 citations
01 Jan 1973
Book•
01 Jan 1973
TL;DR: An approach to the partial-linear realization of finite automata which is independent of the numerous publications on linear automata is presented, which allows to describe more concisely the theory of families of shift-registers and to introduce generalized shift-register realizations.
Abstract: This paper presents an approach to the partial-linear realization of finite automata which is independent of the numerous publications on linear automata. Among other results this theory allows to describe more concisely the theory of families of shift-registers and to introduce generalized shift-register realizations.
Though, for practical reasons, the discussions are restricted to the field GF (2), most of the results may be extended to arbitrary finite fields, some of them to finite rings with unit element.
08 Oct 1973
TL;DR: The main studied problem is: When for the given set Q of finite automata there exists another finite automaton A such that for each automata A′ in Q there exist a subautomaton A″ of A and a homomorphism f of A″ into A′.
Abstract: The main studied problem is: When for the given set Q of finite automata there exists another finite automaton A such that for each automaton A′ in Q there exist a subautomaton A″ of A (we restrict our attention to a special class of subautomata) and a homomorphism f of A″ into A′.