congruence

About the Congruences of Two-Generated Monoid

Authors: Kudryavtseva L. A.

The congruences of two-generated monoid which generated by pair of words of length 2 are considered over two-letter alphabet. It is shown that number of equivalence classes for words of length n is equal to n + 1. The number of words in each class is found.

Morphismes Based on Compatible Tolerances of Finite Automata

Authors: Mangusheva I. P.

It is suggested a method of a construction with the help of some triple of tolerances defined on the sets of states, input and output symbols of an finite definite automaton an another automaton which is connected with the original automaton by a certain morphism.
Considered construction generalizes the known method of finding of the homomorphic images of an automaton with the help of a triple of equivalences, which satisfies to the certain conditions.

Algebraic Properties of Abstract Neural Network

Authors: Slepovichev I. I.

The modern level of neuroinformatics allows to use artificial neural networks for the solution of various applied problems. However many neural network methods put into practice have no strict formal mathematical substantiation, being heuristic algorithms. It imposes certain restrictions on development of neural network methods of the solution of problems. At the same time there is a wide class of mathematical models which are well studied within such disciplines as theory of abstract algebras, graph theory, automata theory.

Principal Ideals in the Congruence Semilattice of a Path

Authors: Fomina E. O.

It is proven that principal ideals generated by congruences of a path having the same type are isomorphic lattices. The number of elements, atoms and coatoms is found for the principal ideal generated by a given congruence of a path.