**FINITE-STATE MACHINES** — the mathematical models intended for approximate display of various really proceeding and abstract processes (phenomena). To. and. systems can be the model of the technical device any biol (e.g., idealized nervous network of an animal). In such models the variables chosen for the description of process (e.g., the frequency or duration of nervous impulses) have discrete values, and dependences between them are defined in these or those specific intervals of time.

Methods and the theory To. and. find application in the most various spheres of human activity, including in medicine (processing of curves of cordial activity, modeling of work of a nervous system, allocation of signs and recognition of diseases, processing of statistical data, etc.), in linguistics (the analysis of syntactic features of languages), in pedagogics (creation of the training and examining automatic machines). Most widely the theory To. and. and the theory of experiments with automatic machines are applied in the analysis and synthesis of discrete devices of automatic equipment and computer facilities, at problem solving of diagnosing of their technical condition.

According to the theory To. and. variables accept final values (quantitative or qualitative). The set of possible combinations of values of entrance variables forms the entrance alphabet, output variables — the output alphabet, and internal variables — a set of internal states of the finite-state machine. It is supposed also that the continuous time scale is divided into intervals (steps) and values of variables are considered only in the timepoints dividing the next steps. These timepoints can be set, e.g., by a special source of the synchronizing signals or the moments of change of values of entrance variables.

On the basis of the theory To. and. study forms of a task of the corresponding mathematical models (automatic machines), problems of minimization of number of states, methods of the analysis and synthesis of automatic machines, the principles and methods of hardware and program implementation, etc. A special branch of the theory To. and. the theory of experiments with automatic machines is, with the help the cut is solved a problem of identification of automatic machines, by definitions of reference and final states, investigate methods of creation of experiments and t. and.

See also Mathematical methods in medicine .

**Bibliography:** Yzerman M. A., etc. Logic, automatic machines, algorithms, M., 1963; TG about z and N. V N. Modeling of neural structures, M., 1970, bibliogr.; Recognition of images and medical diagnosis, under the editorship of Yu. I. Neymark, M., 1972, bibliogr.

*P. P. Parkhomenko.*