Showing papers on "Automata theory published in 1973"

Invertible linear finite automata

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.

A simple technique for structured variable lookup

Abstract: A simple technique for the symbol-table lookup of structured variables based on simple automata theory is presented. The technique offers a deterministic solution to a problem which is currently handled in a nondeterministic manner in PL/I and COBOL compilers.

On multistochastic automata

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.

The Emptiness and Complementation Problems for Automata on Infinite Trees

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.

Loop-free compositions of certain finite automata. II

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.

Model Theoretical Methods in the Theory of Automata.

Abstract: A method for forming a cyan dye image by development of an exposed silver halide photographic material with a developer containing a cyan coupler of the following formula: in which R represents hydrogen atom or an alkyl group having a carbon number of one to twenty; R1 represents an alkylsulfonamide or alkylsulfamoyl group; R2 represents an alkyl, aryl group or a 5 or 6-membered heterocyclic group containing a nitrogen, oxygen or sulfur atom; R3 represents a hydrogen or halogen atom; X represents an alkylene, metaphenylene or orthophenylene group; Z represents a hydrogen atom or a split-off radical; and n has an integral value of one or two.

Remarks on the notion of equivalence of automata

Abstract: In the paper [2] there are given the following definitions: Definition 1. By an automaton (S,X, Y,8,X) we mean the system of three sets S, X, Y and two functions 8:SxX->S, \:SxX-+ Y. Arbitrary automata will be denoted by capital Latin letters. Definition 2. We say that an automaton is homomorphic to the automaton if there exist functions (not necessarily one-to-one) a and b and a one-to-one function c a:S->S;, b:X-+X', c:Y->Y' such that for every pair (s,x}eSxX have a [8 (s, x)] = l'\a (s), b (x)] and c [A (s, x)] = A'[a (s), b (x)] . If the functions a, b, c are one-to-one then the homomorphism of automata will be called isomorphism of automata. We shall write A horn B if the automata A and B are homomorphic and A iz B if the automata are isomorphic. It is easy to see that homomorphism of automata is a transitive relation. In this paper1 we shall give an example of equivalent automata in the sense esta? blished by R. Nowakowski in the paper [3]2; however, if we perform the operation of coupling with retardation on them then they cease being equivalent. It means that the relation of equivalence in the considered sense which is also an equivalence rela? tion in the algebraic sense is not a congruence with respect to the operation of coupl? ing with retardation. Let {0, l}k be the set of all sequences x = (xx,..., xk}, where xt e {0,1}, and k is a positive integer. By the operation of coupling with retardation3 we mean the ope? ration defined in the following way:

Zur theorie der partiell-linearen Realisierungen endlicher Automaten

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.

A general systems theory for studies in cybernetics and automation—part ii

Abstract: Artificial automata replace, in part or in total, natural automata in systems, and properly disciplined models of natural automata become design models of artificial automata for replacement. In Part I, a summary of two sets of disciplines provided by a General Systems Theory is presented, and the importance of these disciplines to the modeling of three inherited abilities is indicated for a case study. A theorem is presented in the form of an algorithm to aid in the modeling of the ability to modify and extend knowledge structures. In Part II (appearing in the next issue), the proof of the theorem is given and the theorem is applied to the case study. Finally, the application of the disciplines of the General Systems Theory is indicated for a second casestudy of an industrial system of 10 interactive automata.

On the Problem of Automata Set Representation

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′.