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   <subfield code="a">An optimal discrete nonlinear logical-dynamical filter-predictor</subfield>
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   <subfield code="a">To quickly identify the mode of operation and estimate the vector of state of a discrete stochastic logical-dynamical plant from the results of their incomplete or inaccurate measurements, a method for synthesizing the optimal structure of estimator of a small order multiple of the order of the observed plant is proposed. Bayesian criteria with various matrix loss functions are considered. To improve the accuracy at each time step, the equation of state of the estimator is divided into two parts (filtering and predicting), and to synthesize the second part, an additional optimality criterion is introduced. Relationships between the optimal structure functions of such a logical-dynamical filter-predictor and the corresponding posterior probability distributions are established, and the relations for determining those posterior probability distributions are found. The methods for constructing the suboptimal structure of this estimator and the possibility of reducing its order by evaluating only the information portion of the large state vector of the plant are discussed.</subfield>
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