The Method of Mathematical Modeling of Cognitive Digital Automata
An approach to solving the problem of mathematical modeling of cognitive digital automata (CDA) is proposed. The task of formalizing the concept of the cognitive nature of the CDA mathematical model comes to the fore. The cognitiveness (cognition) of the mathematical model is determined by the possibility of learning and generating solutions that are not provided for in the learning process. A special feature of CDA is that the description of the neural network (NN) structure is used as a structural circuit of the automata, and the logical function "NOTANDOR" is used as the model of the neuron. In the case of the feedbacks formation from the output to the inputs of the neurons, the model of the neuron is a binary trigger with a logical function "NOTANDOR" at the input. As a tool for constructing a mathematical model of CDA, a mathematical apparatus of Petri nets (PNs) is proposed: marked graphs, inhibitory PNs and PNs with programmable logic. The mathematical model is builton the basis of the representation of the CDA in the form of the state equation of the PNs from the class of Murat equations (matrix equations) or a system of linear algebraic equations. The task of formalizing the concept of cognitiveness (cognition) is solved as a result of the logic synthesis (learning) of the initial structural circuit of CDA or the formation of the formula (network algorithm) of CDA. At the same time, the possibility of forming a formula (network algorithm) of CDA depends on the critical mass (quality) of training sets and training algorithms. Hence, the task of generating the minimum set of training sets for a given CDA function or experimentally determined function takes on particular importance. Forecasting or generation of solutions, in turn, is performed on the basis of the mathematical model of CDA obtained in the learning process. intellectual control system, cognitive digital automata, artificial intelligence, neural networks, machine learning, cognition, Petri nets, equation of states, mathematical modeling, synthesis, generation, analysis, logic.
