Problem of Synthesis of Minimal Forms of Logical Functions

Abstract

In this paper, we consider special classes of corrective functions, sets of heuristic algorithms that allow errors in the calculation of elementary properties. The article solves the problem of logical separability for the correcting functions of multivalued logic. For not everywhere defined functions, the simplest, in a sense, extensions to the entire set are constructed in such a way that these extensions are everywhere defined functions of many-valued logic. When solving a wide class of practical problems, the algorithms are often used that allow errors in calculation of elementary properties or refusals to solve problems. In such cases, several incorrect algorithms are usually applied to solve a single problem, and then a corrective function is constructed. Since the result of computing an elementary property can be either a refusal to calculate, or the property is satisfied, or the property is not satisfied, the corrective function is a function of a threedigit logic. For substantive reasons, the set of corrective functions should be limited. The problem of constructing an optimal corrector for heuristic algorithms is outlined in the paper. The aspect of corrective function continuation is considered. The problem is solved on selecting all the vertices of the grids not included into the definition domain of a previously constructed correctors.