Article

Algorithms for Minimizing Disjunctions of Complex Conjunctions Based on First-Order Neighborhood Information for Solving Systems of Boolean Equations

Anvar KabulovNational University of Uzbekistan,Faculty of Applied Mathematics and Intelligent Technologies,Tashkent,UzbekistanAbdussattar BaizhumanovSouth Kazakhstan State Pedagogical University,The department of Mathematics,Shymkent,KazakhstanIslambek SaymanovNational University of Uzbekistan,Faculty of Applied Mathematics and Intelligent Technologies,Tashkent,UzbekistanMansur BerdimurodovNational University of Uzbekistan,Faculty of Applied Mathematics and Intelligent Technologies,Tashkent,Uzbekistan

2022en

ABI

Abstract

The neighborhoods of the 1st order of disjunctions of complex conjunctions of logical statements of systems of nonlinear Boolean equations given by Zhegalkin polynomials are investigated. A method for minimizing disjunctions based on the absorption of complex conjunctions by a first-order neighborhood is proposed. For this, criteria for the absorption of complex conjunctions by a first-order neighborhood are proved, similarly to the theory of Y.I.Zhuravlev on the absorption of elementary conjunctions in the class of disjunctive normal forms of Boolean functions. An algorithm for minimizing the disjunctions of complex conjunctions based on a neighborhood of the 1st order is developed.

Topics

Advanced Computational Techniques in Science and Engineering Mathematical Analysis and Transform Methods Advanced Data Processing Techniques

Identifiers

DOI: 10.1109/icsintesa56431.2022.10041529

Citations and references

Cited by 2 27 references

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