Stochastic automats action's asymptotic features in stationar random environment

Finite automats are useful objects, used for building of a complex mathematical models. In this kind of systems, deterministic and finite automats with stochastic (probabilistic) structure can be described as simple objects. The most interesting kind of automats are the ones, which acts are advisable and its structure does not contain any kind of information about the environment, in which it is functioning. This kind of automats must guarantee the following symmetry feature: in the case of similar sequence of the input signals, when automat is executing different kind of actions on its input, automat’s behavior must be identical. As studies show, it is practically impossible to build an automat, which will be optimal to any parameters, in any kind of environment. Therefore it is very important to build different kind of automats constructions and elaborate analytical and numerical methods to calculate its probabilistic behaviors in a random environment. In the master’s thesis the examined things are: functioning of the special class’ finite stochastic automats, in the stationary random environment which reacts with responses on automat’s actions and this responses are perceived by the automats like one of the following reactions from the three type of classes’ possible reactions: 1. Class with desired reactions (win, award) 2. Class with non-desired reactions (loss, fine) 3. Class with neutral reactions (indifferent) Finite stochastic automat’s functionality descriptor, Markov chain spectral localization problem is solved in this kind of environment. Particularly, depending on the environment’s parameters, the existence and uniqueness of the eigenvalue, which’s module strives toward to 1 (in the case of infinite increase of the automat’s memory) is estimated. Based on the producing function, sequence convergence of the finite automats to the infinite automat (which has the similar structure) is estimated, together with the available asymptotic action’s complete classification. The functionality of the wider class’ infinite stochastic automats functionality, in the stationary stochastic environment which has reactions of the 3 classes, is also described, and the numerical algorithm which calculates its actions’ probabilistic characteristics is implemented. Machine experiments are held regarding the above mentioned issues and the analysis of the obtained results are provided in the thesis.

Lecture files: