ISSN 1991-2927

 V. Kozhevnikov
 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 "NOT-AND-OR" 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 "NOT-AND-OR" 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.
 2019_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling, Artificial intelligence.

 V. Kozhevnikov
 Reachability Analysis Method of Digital Automata Logic Circuits Stable States The method is based on representation of digital automata logic circuits in the form of Petri nets state equations of Murata equations class. The inhibitory Petri nets are used for the digital automata logic simulation. Inhibitory Petri nets provide the most accurate simulation of logic circuits but lose their basic properties at a rather high modeling capacities and have the lower capacity of resolution compared to classical Petri nets. The problem solving is achieved by the inhibitory Petri nets presentation as matrix equations with implicit specified inhibitory arcs in the incidence matrix. The Petri nets graphics is used as a transition tool from the initial description of the automata to its representation as an equation of Petri nets states or as a set of linear algebraic equations. The digital automata network model-building is performed on the base of a homogeneous data flow conservation. Homogeneity property of the network model provides preservation of the inhibitory Petri nets properties in the network model to simulate the logic and simultaneously serves as a criterion of stable states reachability. Reachability analysis of logic circuits stable states comes down to solving the equation of Petri nets states at the given reachability criteria. The method can be used for solving the basic structural circuit automata logic synthesis tasks, test generation, simulation, faults modeling and computation, fault-tolerance and reliability analysis of automata logic circuits.Method, analysis, reachability, digital automata, logic circuits, petri nets, equation of states, stable states.
 2014_ 1

Sections: Electronic and electrical engineering

Subjects: Electrical engineering and electronics.

 V. Kozhevnikov
 The Accessibility-analysis Method of Inhibitory Petri Nets The paper presents the research findings for the problem solving of the accessibility analysis of inhibitory Petri nets. The method is based on the orthogonal characteristic of the network. The method makes it possible to analyze both conventional and inhibitory Petri netsMethod, analysis, logic, inhibitory petri nets, an equation of state.
 2013_ 3

Sections: Mathematical modeling, calculi of approximations and software systems

Subjects: Mathematical modeling.

 V. Kozhevnikov
 Method of Mathematical Modeling of Logic Circuitsof Digital Automata The method is based on the presentation of digital automata in the form of Petri-net state equations of Murata equation class. The paper shows a logical aspect in mathematical modeling of digital automata. The suggested method provides possible analytical and simulation modeling of logic circuits for digital automata. Modeling of logic circuits of digital automata comes down to solving Petri-net state equations.Method, modeling, digital automata, logic circuit, petri net, state equations.
 2012_ 4

Sections: Software and mathematical support of computers, computer systems and networks

Subjects: Mathematical modeling, Automated control systems, Computer-aided engineering.

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