On finite moore geometries

Conditions are given which must be satisfied by the parameters of a Moore geometry. It is shown that there are no nontrivial Moore geometries of diameter 3.     

On free and torsion-free automata

In this paper we define free, torsion-free and torsion-free completely on an automaton. We prove some properties of them which are important     

On the existence of certain generalized moore geometries (Part IV)

It is shown that generalized Moore geometries of type GM₄(s, t, s + 1), with st > 1, do not exist.     

Groups generated by 3-state automata over a 2-letter alphabet. II

This is the second in a series of papers presenting results on the classification of groups generated by 3-state automata over a 2-letter alphabet. Among the examples treated here, one can find automata generating the free product of 3 cyclic groups of order 2, a virtually free abelian group of rank 3, a solvable group of derived length 3, some virtually torsion-free weakly branch groups, and other interesting self-similar groups. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 50, Functional Analysis, 2007.     

On concrete characterization of universal hypergraphic automata

In this paper, we consider structured automata without output signals whose state sets are endowed with an algebraic structure of hypergraphs. The main result of the paper is a theorem where we obtain necessary and sufficient conditions for the possibility of defining on the state set of some automaton A a structure of a hypergraph H such that the automaton A will be the universal hypergraphic automaton.     

On the free automata and tensor product

In this paper we shall introduce the algebraic structure of a tensor product for arbitrarily given automata, giving a defintion of the tensor product for automata. We introduce and study that for any setX there always exists a free automaton onX. The existence of a tensor product for automata will be investigated in the same way like modules do.     

On an expansion of nondeterministic finite automata

We consider a possible generalization of nondeterministic finite automata. The goals of this consideration are: to apply some obtained algorithms for various problems of minimization of classical nondeterministic automata; to use such automata for describing practical anytime algorithms for the same problems of minimization; to simplify some proofs for algorithms of simplification for usual nondeterministic automata.     

On associative curves. II

Acta Mathematica Hungarica -     

On Brown Polynomials. II

The results of the author’s previous article are improved. We also establish that each irreducible polynomial over a Henselian valued field is a Brown polynomial.