автоматы

Solving Some Problems of Automata Behaviour Analysis

Authors: Tyapaev L. B.

In the context of the geometrical approach and by means of geometrical methods automaton behaviour is studied as curves on the plane. The attention is called to a new way of setting the finite-state machines as a functional curve on the plane. Also within the limits of the geometrical approach problems of automaton analysis, synthesis, diagnosis and transformation have been also investigated. 

Discrete Dynamical Systems Defined Geometrical Images of Automata

Authors: Tyapaev L. B., Vasilenko D. V., Karandashov M. V.

 The object of study is the dynamic system defined by geometrical images of automata. The phase space of the system is determined by orthogonal and affine transformations of geometric images. Compositions of dynamical systems of a given type and their characteristics are studied. 

Automata on algebraic structures

Authors: Skobelev V. V.

A survey of results obtained in investigations of automata determined over finite algebraic structures. The objects of research are automata over some finite ring, automata determined in terms of ideals, automata over varieties, and families of hash-functions determined by automata without output function. Computational security, complexity of simulation and homomorphisms of investigated automata are characterized. 

Representation of universal planar automata by autonomous input signals

Authors: Molchanov V. A.

Universal planar automata are universally attracted objects in the category of automata, whose sets of states and output signals are endowed with structures of planes. The main result of the paper shows that any universal planar automaton is isomorphic to a many-sorted algebraic system canonically constructed from autonomous input signals of the automaton.