SOLUTION OF SYSTEMS OF
NONLINEAR BOOLEAN EQUATIONS

Abstract

The paper proposes the methods and a software package for solving systems of Boolean equations, the propositions of which are formulas over an arbitrary basis, Zhegalkin polynomials consisting of nonlinear components and disjunctive normal forms.

The formation of Zhegalkin polynomials from formulas over an arbitrary basis, the finding of the maximum joint subsystems of logical equations and the search for intersections of the sets of solutions of several subsystems of the system of equations are considered.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 3
Year: 2021

DOI: 10.12732/ijam.v34i3.13

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References

  1. [1] A.V. Kabulov, A.A. Bayzhumanov, Some issues of analytical transformations in minimization of logical functions, Questions in Computational and Applied Mathematics, Tashkent, RISO AN UzSSR, 65 (1981).
  2. [2] A.V. Kabulov, A.A. Bayzhumanov, Representation of logical operations in the decimal system of calculus, Algorithms, Tashkent, RISO AN UzSSR, 45 (1981).
  3. [3] A.V. Kabulov, A.A. Bayzhumanov, A new approach to solving systems of Boolean equations, Proceedings of the X Conference of Young Scientists in the NPO Cybernetics of the Academy of Sciences of the Uzbek SSR, 76 (1982).
  4. [4] A.V. Kabulov, I.H. Normatov, About problems of decoding and searching for the maximum upper zero of discrete monotone functions, Journal of Physics: Conference Series, 1260 (2019), # 102006.
  5. [5] A.V. Kabulov, E. Urunbaev, A.O. Ashurov, Logical method for constructing the optimal corrector of fuzzy heuristic algorithms, 2019 Interna- tional Conference on Information Science and Communications Technolo- gies (ICISCT), 1210 (2019), 1-4.
  6. [6] A.V. Kabulov, I.H. Normatov, A.O. Ashurov, Computational methods of minimization of multiple functions, Journal of Physics: Conference Series, 1260 (2019), # 102007.
  7. [7] A.V. Kabulov, I.H. Normatov, A. Karimov, Algorithmization control of complex systems based on functioning tables, Journal of Physics: Conference Series, 1441 (2020), # 012141.
  8. [8] A.V. Kabulov, I.H. Normatov, E. Urunbaev, A.O. Ashurov, About the problem of minimal tests searching, Advances in Mathematics: Scientific Journal, 9 (2020), 10419-10430.
  9. [9] A.V. Kabulov, I.H. Normatov, E. Urunbaev, A.O. Ashurov, Synthesis methods of optimal discrete corrective functions, Advances in Mathematics: Scientific Journal, 9 (2020), 6467-6482.