• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.851-858
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• 1999

A new problem of the theory of finite automata (Rabin-Scott's automata) is considered. So called basis automaton for the given regular language l is defined. this automaton is unique for the given L, it is defined by two au-tomata of canonical form: for L and for its inverse language LR. Some properties of basis automata are considered. Such properties make these automata most convenient for using in some special tasks dealing with the given regular language.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.551-558
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• 2004

We shall discuss some properties of quasi-homomorphisms associated with automata. We shall give some characterizations in terms of characteristic semigroups for regular and invertible attomata.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.483-497
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• 2024

Isometric array grammar is one of the simplest model to generate picture languages, since both sides of its production rule have the same shape. In this paper, we have introduced isometric fuzzy regular array grammars to generate isometric fuzzy regular array languages and discussed its closure properties. Also, the relation between isometric fuzzy regular array grammar and boustrophedon fuzzy finite automata has been discussed. Moreover, we study the relation between two dimensional fuzzy regular grammars with returning fuzzy finite automata and boustrophedon fuzzy finite automata. Further, the hierarchy results of these three classes of languages have been discussed.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.693-703
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• 2001

In this paper we consider non-deterministic finite Rabin-Scott’s automata. We use a special structure to descibe all the possible edges of non-determinstic finite automaton defining the given regular language. Such structure can be used for solving various problems of finite automata theory. One of these problems is edge-minimization of non-deterministic automata. As we have not touched this problem before, we obtain here two versions of the algorithm for solving this problem to continue previous series of articles.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.645-655
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• 2002

In this Paper we consider non-deterministic finite Rabin-Scott's automata. We define special abstract objects, being pairs of values of states-marking functions. On the basis of these objects as the states of automaton, we define its edges; the obtained structure is considered also as a non-deterministic automaton. We prove, that any edge of any non-deterministic automaton defining the given regular language can be obtained by such techniques. Such structure can be used for solving various problems in the frames of finite automata theory.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.747-756
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• 1999

In ring theory it is well-known that a ring R is (von Neumann) regular if and only if all right R-modules are flat. But the analogous statement for this result does not hold for a monoid S. Hence, in sense of S-acts, Liu (]10]) showed that, as a weak analogue of this result, a monoid S is regular if and only if all left S-acts satisfying condition (E) ([6]) are flat. Moreover, Bulmann-Fleming ([6]) showed that x is a regular element of a monoid S iff the cyclic right S-act S/p(x, x2) is flat. In this paper, we show that the analogue of this result can be held for automata and them characterize regular semigroups by flat automata.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.887-894
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• 2000

In this paper we consider the corrected version of the algorithm of the state-minimization for the nondeterministic finite automata: we correct here a mistake of the previous paper, where the same problem was considered.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.135-150
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• 2002

The present paper discusses non-deterministic finite Rabin-scott's automate. The majority of works recently dealing with this subject were, in fact, concerned only with properties of a canonical term automata or of some objects equivalent to it. This article continues the series of works in which the authors state a different point of view, describing the finite automata as just another invariant of the given regular language called basis finite automaton. In this article the authors argue on some new properties for the basis finite automaton. One of them is included into basis automaton's table of binary relations. It is stated that this table can not contain either identical strings or identical columns. Another property depicts a possibility to obtain any finite automaton for a given regular language by the process of duplicating or combining some of its states.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.783-798
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• 1999

Nondeterministic finite Rabin-Scott's automata without initial and final states (2 $\omega$-FA) are considered. In this paper they are used to define so called sets of obstruction used also in various alge-braic systems and to consider similar problems for the formal languages theory. Thus we define sets of obstructions of languages(or, rather, 2$\omega$-languages) of such automata. We obtain that each 2$\omega$-language defined by 2 $\omega$-FA has the set of obstruction being a regular language. And vice versa for each regular language L(containing no proper subword of its another word) there exists a 2$\omega$ -FA having L as the set of obstructions.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.379-392
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• 1999

The problem of the state-minimization for the nonde-terministic finite Rabin-Scott's automata is considered. A new algo-rithm for this problem is obtained. The obtained algorithm has the exponential effectiveness like the earlier-known algorithms for this problem. But each of previous algo-rithms amounts to the search of minimum generative system for local reaction of equal automaton of canonical form and unlike them we use in this paper two special function marking states of the given automaton.