геометрический образ

Geometrical images of finite state machines

Authors: Tverdokhlebov V. A.

In this work a new way of defining finite state machines (FSM) is being suggested. The discrete word geometry is built for that purpose, in which machine image is expressed as a set of lines. The methods of synthesis and analysis of geometrical images of FSMs and their features are researched. The new way of defining the FSMs allows analyzing the machine's behavior, excluding the exhausting recursive procedure of defining the initial fragments of machine functioning.

The Geometric Form of Automaton Mappings, Recurrent and Z-recurrent Definition of Sequences

Authors: Tverdokhlebov V. A.

For automaton mappings we present a method to construct geometric images, a method for complexity estimate by geometric forms, a method of Z-recurrent definition of sequences. A method for complexity estimate for finite sequences by recurrent and Z-recurrent numerical indicators is proposed. Numerical indicators of recurrent and Z-recurrent definitions of sequences are systematized into the spectrum of recurrent definitions with 5 levels of numerical indicators.

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.