On the minimization of k-valued logic functions in the class of disjunctive normal forms
DOI:
https://doi.org/10.26577/JMMCS202412114Keywords:
k-valued, minimization, disjunctive normal form, rank, abbreviated d.n.f., monotone functionAbstract
In the world, research devoted to adjusting the results of heuristic methods based on forecasting, recognition, classification, and determining the absolute extremum of a multidimensional function is relevant and widely used in such fields as medicine, geology, hydrology, management, and computer technology. In this regard, it is important to construct optimal correctors of heuristic algorithms based on control materials. Therefore, checking the completeness of classes of k valued logical functions and developing methods and algorithms for minimizing functions in the class of canonical normal forms, estimating the number of monotonic functions of k valued logic, constructing minimal bases of special classes of correcting functions for correcting incorrect algorithms remains one of the important problems of computational and discrete science. mathematics. Currently, a lot of scientific research is being carried out around the world aimed at expanding the integration of science and industry, in particular the development of the theory of k-valued logical functions for correcting the results of heuristic algorithms. In this case, an important role is played by the construction of formulas in the class of canonical normal forms, the coding of elementary conjunctions and the application of the rules of gluing, absorption and idempotency for them, and checking the completeness of systems of correcting functions. Consequently, the development of effective numerical computational methods and algorithmsfor constructing correction functions based on k-valued logic to improve the accuracy of the results of heuristic methods is considered a targeted scientific research. The paper considers the
representation of k-valued logical functions in the class of disjunctive normal forms. Various classes of monotone functions of k-valued logic are studied. Theorems are proved on the coincidence of abbreviated and shortest disjunctive normal forms of k-valued functions. For a certain class of k-valued monotone functions, we prove an estimate for the number of functions from this class. criteria for the absorption of elementary conjunctions by a first-order neighborhood of disjunctive normal forms of k-valued functions are proved
References
A. Kabulov, I. Yarashov, A. Otakhonov Algorithmic Analysis of the System Based on the Functioning Table and
Information Security // 2022 IEEE International IOT, Electronics and Mechatronics Conference (IEMTRONICS),
Toronto, ON, Canada, 2022, pp. 1-5, doi: 10.1109/IEMTRONICS55184.2022.9795746.
A. Kabulov, I. Saymanov, I. Yarashov, A. Karimov Using Algorithmic Modeling to Control User Access Based on
Functioning Table // 2022 IEEE International IOT, Electronics and Mechatronics Conference (IEMTRONICS), Toronto,
ON, Canada, 2022, pp. 1-5, doi: 10.1109/IEMTRONICS55184.2022.9795850.
E. Navruzov, A. Kabulov Detection and analysis types of DDoS attack // 2022 IEEE International
IOT, Electronics and Mechatronics Conference (IEMTRONICS), Toronto, ON, Canada, 2022, pp. 1-7, doi:
1109/IEMTRONICS55184.2022.9795729.
A. Kabulov, I. Saymanov, I. Yarashov and F. Muxammadiev Algorithmic method of security of the Internet of Things based
on steganographic coding // 2021 IEEE International IOT, Electronics and Mechatronics Conference (IEMTRONICS),
Toronto, ON, Canada, 2021, pp. 1-5, doi: 10.1109/IEMTRONICS52119.2021.9422588.
A. Kabulov, I. Normatov, E. Urunbaev, F. Muhammadiev Invariant Continuation of Discrete Multi-Valued Functions
and Their Implementation // 2021 IEEE International IOT, Electronics and Mechatronics Conference (IEMTRONICS),
Toronto, ON, Canada, 2021, pp. 1-6, doi: 10.1109/IEMTRONICS52119.2021.9422486.
A. Kabulov, I. Normatov, A. Seytov, A. Kudaybergenov Optimal Management of Water Resources in Large Main
Canals with Cascade Pumping Stations // 2020 IEEE International IOT, Electronics and Mechatronics Conference
(IEMTRONICS), Vancouver, BC, Canada, 2020, pp. 1-4, doi: 10.1109/IEMTRONICS51293.2020.9216402.
Kabulov, A. V., Normatov, I. H. (2019). About problems of decoding and searching for the maximum upper zero
of discrete monotone functions // Journal of Physics: Conference Series, 1260(10), 102006, 2019. doi:10.1088/1742
/1260/10/102006.
Kabulov, A. V., Normatov, I. H., Ashurov A.O. Computational methods of minimization of multiple functions // Journal
of Physics: Conference Series, 1260(10), 10200, 2019. doi:10.1088/1742-6596/1260/10/102007.
Anvar Kabulov, Alimdzhan Babadzhanov, Islambek Saymanov Correct models of families of algorithms for calculating
estimates // AIP Conference Proceedings 8 June 2023; 2781 (1): 020010. https://doi.org/10.1063/5.0144830.
Anvar Kabulov, Alimdzhan Babadzhanov, Islambek Saymanov Completeness of the linear closure of the voting model //
AIP Conference Proceedings 8 June 2023; 2781 (1): 020020. https://doi.org/10.1063/5.0144832.
Anvar Kabulov, Mansur Berdimurodov Gost R 34.12-2015 (Kuznechik) analysis of a cryptographic algorithm // AIP
Conference Proceedings 8 June 2023; 2781 (1): 020046. https://doi.org/10.1063/5.0145975.
Valeri Sklyarov, Iouliia Skliarova, Anvar Kabulov Hardware accelerators for solving computationally intensive
problems over binary vectors and matrices // AIP Conference Proceedings 8 June 2023; 2781 (1): 020013.
https://doi.org/10.1063/5.0145125.
Preface: International Conference on Modern Problems of Applied Mathematics and Information Technology // AIP
Conference Proceedings 8 June 2023; 2781 (1): 010001. https://doi.org/10.1063/12.0017180.
Normatov I. Principle of Independence of Continuation of Functions Multivalued Logic from Coding // Journal of Physics:
Conference Series, 2019, 1210(1), 012107. doi:10.1088/1742-6596/1210/1/012107.
I. Normatov, E. Kamolov Development of an algorithm for optimizing the technological process of kaolin enrichment //
IEEE International IOT, Electronics and Mechatronics Conference (IEMTRONICS), Vancouver, BC, Canada, 2020,
pp. 1-4, doi: 10.1109/IEMTRONICS51293.2020.9216371
