автомат

On Definability of Universal Graphic Automata by Their Input Symbol Semigroups

Authors: Farakhutdinov R. A., Molchanov V. A.

Universal graphic automaton Atm(G, G′ ) is the universally attracting object in the category of automata, for which the set of states is equipped with the structure of a graph G and the set of output symbols is equipped with the structure of a graph G′ preserved by transition and output functions of the automata. The input symbol semigroup of the automaton is S(G, G′ ) = End G×Hom(G, G′ ). It can be considered as a derivative algebraic system of the mathematical object Atm(G, G′ ) which contains useful information about the initial automaton.

On Problem of Abstract Characterization of Universal Hypergraphic Automata

Authors: Molchanov V. A., Khvorostukhina E. V.

Hypergraphic automata are automata whose state sets and sets of output symbols are endowed with algebraic structures of hypergraphs preserving by transition and exit functions. Universally attracting objects in the category of hypergraphic automata are automata Atm (H1,H2), where H1 is a hypergraph of the state set, H2 is a hypergraph of the set of output symbols and S = EndH1 × Hom(H1,H2) is a semigroup of input symbols. Such automata are called universal hypergraphic automata.

Abstract Characterization of Semigroups of Input Signals of Universal Planar Automata

Authors: Molchanov V. A.

Universal planar automata are universally attracted objects in the category of automata, for which sets of states and output signals are endowed with structures of planes. The main results of the paper give us necessary and sufficient conditions under which an arbitrary automaton is isomorphic to a universal planar automaton and an arbitrary semigroup is isomorphic to the semigroup of input signals of a universal planar automata.

 

Affine transformations of geometrical images of finite automata

Authors: Matov D. O.

A subclass of affine transformations on the set of geometrical images of finite automata is investigated. The results about the characteristics and the form of these transformations are described. 

Identification of a state machine structure with finites fragment of behavior

Authors: Bogomolov S. A.

 Identification of a state machine structure with finite fragments of behavior is discussed. The state machine behavior is a set of various finite-sequential (f.-s.) functions realized in a state machine, and under a finite fragment of behavior we mean traces of f.-s. functions and state machines. The concept of an identifying trace for a state machine irredundant over its realization is introduced.