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The article offers mathematical tools for programming dispatcher tasks on programmable logic matrices, which allow to obtain closed axiomatic models of the dispatcher’s professional activity in the course of the dispatcher’s dialogue with the computer and implement it in the form of optimal combinational logic schemes with pairwise alternative outputs. These tools implement a user-friendly interface for modeling a logically complete consistent system of axioms written in the production language in a tabular form that resembles decision tables with a limited input. The modeling dialog completely frees the dispatcher from the need to know the properties of axiomatic models and requires only professional skills of dispatcher management. Its function in this dialogue is only to specify the desired action in a specific situation that occurs during the object management process. Such situations are constantly formed during the field work in crop production. Sudden failure of power units, two or three-day period of adverse weather increases the risk of violation of agricultural deadlines. This requires prompt decision - making on re-completing units, changing the plan of mechanized work. The search of all possible situations and obtaining on their basis an optimal set of consistent products closing the axiomatic model is provided exclusively by the interface software, which is developed using algorithms for negating and minimizing disjunctive normal forms of logical functions and includes software tools for modeling logically complete consistent decision tables and optimizing them in order to obtain optimal combinational logical devices with their subsequent hardware implementation in the form of microchips. In addition, these software tools are offered as one of the tools for software implementation of branched algorithms with high complexity indicators according to M. V. Arapov in the automated design of control systems for various purposes.

The game task of confrontation of the attacked hardware-redundant dynamic system with an attacking enemy operating in conditions of incomplete information about the behavior of the attacked enemy in the process of conflict was posed and solved numerically and analytically. The attacking party aspires to increase the intensity of the failures of the components of the attacked system at the expense of its attack resources, up to its total failure. The attacked party, due to the corresponding strategy of redistribution of reserve blocks of the hardware-redundant dynamic system between the failed main blocks at the appropriate instants of time, strives to maximize the probability of failure-free operation of the attacked system at the end of the confrontation (game) with the attacking enemy. Behavior of the system under attack in the process of conflict is approximated by the Markov process, and the number of operable states is equal to the number of failed functional blocks that do not exceed the number of standby blocks. As a payment function in the game in question, the probability of failure-free operation of the attacked system is used by the time the game ends. The solution of the game is the vector of the system setup moments after the corresponding failures of the functional blocks and the set of reservation vectors corresponding to the instantaneous settings of the system being attacked, which maximizes the probability of system failure during the conflict. The differential game model is reduced to a multi-step matrix model with given probabilities of the states of the attacking enemy. Numerical algorithms for calculating the vector of reservation for the attacked system that maximizes the probability of its trouble-free operation by the end of the game and for solving the game problem in question are presented in a form convenient for implementation on a personal computer.