Showing papers by "Andrei V. Kelarev published in 2004"

Labelled Cayley graphs and minimal automata

Abstract: Cayley graphs considered as language recognisers are as powerful as the more general finite state automata. This paper applies Cayley graphs to define a class of automata and describe minimal automata of this type, all their congruences and the Nerode equivalence of states.

A combinatorial property and power graphs of semigroups

Abstract: Research on combinatorial properties of sequences in groups and semigroups originates from Bernhard Neumann's theorem answering a question of Paul Erd"{o}s. For results on related combinatorial properties of sequences in semigroups we refer to the book [3]. In 2000 the authors introduced a new combinatorial property and described all groups satisfying it. The present paper extends this result to all semigroups.

An Algorithm for Commutative Semigroup Algebras Which are Principal Ideal Rings

Abstract: We outline several algorithms for computing with semigroup representations, and combine them in order to verify when certain algebras are principal ideal rings.

Directed graphs and minimum distances of error-correcting codes in matrix rings

Abstract: The main theorems of this paper give sharp upper bounds for the minimum distances of one-sided ideals in structural matrix rings defined by directed graphs. It is very well known that additional algebraic structure can give advantages for coding applications (see, for example, [8]). Serious attention in the literature has been devoted to considering properties of ideals in various ring constructions essential from the point of view of coding theory (see the survey [7] and books [4], [9], [10]). The investigation of code properties of ideals in structural matrix rings of directed graphs was begun in [6], where two-sided ideals are considered. The aim of this paper is to strengthen the results of [6] and obtain sharp upper bounds for the minimum distances of one–sided ideals in structural matrix rings defined by directed graphs. Let F be a finite field. Throughout, the word graph means a directed graph without multiple edges but possibly with loops, and D = (V, E) stands for a graph with the set V = {1, 2, . . . , n} of vertices and the set E of edges. Edges of D correspond to the standard elementary matrices of the algebra Mn(F ) of all (n×n)– matrices over F . Namely, for (i, j) ∈ E ⊆ V × V , let e(i,j) = ei,j = eij be the standard elementary matrix. Note that ei,jek,l = { 0 if j ̸= k, ei,l if j = k. Denote by MD(F ) = ⊕

On the structure of incidence rings of group automata

Abstract: The Jacobson radical is one of the major tools used in the investigation of the structure of rings and ring constructions. Our main theorem gives a complete description of the Jacobson radicals of incidence rings of group automata for all finite nilpotent groups.

On genetic algorithms minimizing a class of FSA with fuzzy automata

Abstract: Finite state automata are crucial for numerous practical algorithms of computer science. We show how to use genetic algorithms and fuzzy automata to simplify a class of FSA defined by labeled graphs and considered in computer science and engineering literature.

Labelled Cayley graphs and minimal automata

Abstract: Cayley graphs considered as language recognisers are as powerful as the more general finite state automata. This paper applies Cayley graphs to define a class of automata and describe minimal automata of this type, all their congruences and the Nerode equivalence of states.