Synthesis of Optimal Correction Functions in the Class of Disjunctive Normal Forms

Anvar Kabulov, Abdussattar Baizhumanov and Islambek Saymanov ()
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Anvar Kabulov: School of Mathematics and Natural Sciences, New Uzbekistan University, Mustaqillik Ave. 54, Tashkent 100007, Uzbekistan
Abdussattar Baizhumanov: Department of Mathematics, O. Zhanibekov South Kazakhstan State Pedagogical University, A. Baitursynov Street No.13, Shymkent City 160012, Kazakhstan
Islambek Saymanov: School of Mathematics and Natural Sciences, New Uzbekistan University, Mustaqillik Ave. 54, Tashkent 100007, Uzbekistan

Mathematics, 2024, vol. 12, issue 13, 1-17

Abstract: The paper proposes to consider individual heuristics as unreliably operating parts of the information processing system. In a separate case, several different heuristics are adopted to solve the same problem, and the results obtained are adjusted in a certain way. In this case, problems arise that are close in methodology to the problems of synthesizing reliable circuits from unreliable elements or making a collective expert decision. The work solves the problem of constructing an optimal correction function based on control material; classes of functions of k -valued logic under monotonicity restrictions are studied. A theorem on the completeness of the class of monotonic functions of k -valued logic for arbitrary k is proved, and a basis in the given class is proved and constructed. The problem of constructing an optimal corrector in the class of disjunctive normal forms of k -valued functions is solved.

Keywords: disjunctive normal forms; k -valued function; optimal correction function; minimization; logic function; logical separability problem; monotone (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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