Recovery of a dynamic system from its functioning is a problem of current interest in the theory of control systems. As a behavior model of gene network regulatory circuit, a discrete dynamic system has been proposed, where coordinates correspond to the concentration of substances, while special functions, which depend on the system value in the previous moment, account for their increase or decrease. Pseudo-polynomial discrete dynamic system recovery algorithms with additive and multiplicative functions have been obtained earlier. The generalized case of arbitrary threshold functions is considered in this article. Algorithms for significant variables recovery and threshold functions weight regulation, having pseudo-polynomial testing complexity, are given. These algorithms allow one either to recover the system completely, or to lower the threshold function dimension.
This article discusses some approaches to the recognition of the parameters of the threshold k-valued functions, which can be used for building information processing and security units. The main focus is put on the issue of proving k-valued function belonging to the threshold class. For solving this problem it is proposed to use the input coefficients of expansion and increase. With the help of the latter, the coefficients of linear forms of the k-valued threshold function are procedurally approximated. Along with the proposed analytical approach, the article discusses an algorithmic method based on reducing the problem of finding a threshold representation of k-valued functions to the system of linear inequalities, for the solution of which the ellipsoid method, modified by Khachiyan, is applied. The comparative analysis of the proposed methods is carried out based on experiments.
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