Екiншi дәрежелi сызықты емес теңдеулер жүйесiнiң арнайы кластарын шешудiң оңтайлы әдiсi
DOI:
https://doi.org/10.26577/JMMCS.2023.v118.i2.02Кілттік сөздер:
Жегалкин көпмүшесi, сызықтық логикалық функциялар, бiртектi- бiрлiк матрицалар, көпмүшелiк ұзындық, арнайы дизъюнктивтi қалыпты формаларАннотация
Белгiлеулердi жеңiлдету және логикалық теңдеулер жүйелерiн шешу уақытын қысқарту мақсатында екiншi дәрежелi сызықты емес логикалық теңдеулер жүйесiнiң арнайы класын шешу үшiн оңтайлы әдiс ұсынылды. Зерттелетiн сызықты емес логикалық теңдеулер жүйелерiнiң класында логикалық формулалар кейбiр сызықтық қосындыларға толығымен немесе iшiнара бөлiнедi. Нәтижесiнде логикалық формулалар сызықтық көпмүшелердiң көбейтiндiсiне келтiрiледi, оның негiзiнде екiншi реттi логикалық теңдеулер жүйесiне қарағанда шама ретi оңай шешiлетiн сызықтық логикалық теңдеулер жүйесi алынады және арнайы кластың екiншi дәрежелi Жегалкин көпмүшелiгiнен алынған арнайы дизъюнктивтiк қалыпты формалар үшiн кейбiр минимизациялау мәселелерi қарастырылады.
Библиографиялық сілтемелер
[1] A. Kabulov, I. Yarashov and 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
[2] A. Kabulov, I. Saymanov, I. Yarashov and 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
[3] E. Navruzov and 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: 10.1109/IEMTRONICS55184.2022.9795729.
[4] 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.
[5] A. Kabulov, I. Normatov, E. Urunbaev and 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.
[6] A.Kabulov, I. Normatov, A.Seytov and 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.
[7] 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. doi:10.1088/1742-6596/1260/10/102006
[8] Kabulov, A.V., Normatov, I.H. Ashurov A.O. (2019). Computational methods of minimization of multiple functions. Journal of Physics: Conference Series, 1260(10), 10200. doi:10.1088/1742-6596/1260/10/102007
[9] Yablonskii S.V. Vvedenie v diskretnuyumatematiku: Ucheb. posobiedlyavuzov. -2e izd., pererab. idop. -M.:Nauka. Glavnayaredaksiyafiziko-matematicheskoy literature, -384 s.
[10] Djukova, E.V., Zhuravlev, Y.I. Monotone Dualization Problem and Its Generalizations: Asymptotic Estimates of the Number of Solutions. Comput. Math. and Math. Phys. 58, 2064–2077 (2018). https://doi.org/10.1134/S0965542518120102
[11] Leont’ev, V.K. Symmetric boolean polynomials. Comput. Math. and Math. Phys. 50, 1447–1458 (2010). https://doi.org/10.1134/S0965542510080142
[12] Nisan, N. and Szegedy, M. (1991). On the Degree of Boolean Functions as Real Polynomials, in preparation.
[13] RamamohanPaturi. 1992. On the degree of polynomials that approximate symmetric Boolean functions (preliminary version). In Proceedings of the twenty-fourth annual ACM symposium on Theory of Computing (STOC ’92). Association for Computing Machinery, New York, NY, USA, 468–474. https://doi.org/10.1145/129712.129758.
[14] Gu J., Purdom P., Franco J., Wah B.W. Algorithms for the satisfiability (SAT) problem:A Survey // DIMACS Series in Discrete Mathematics and Theoretical Computer Science. 1997.Vol. 35. P. 19–152.
[15] Goldberg E., Novikov Y. BerkMin: A Fast and Robust SAT Solver // Automation andTest in Europe (DATE). 2002. P. 142–149.
[2] A. Kabulov, I. Saymanov, I. Yarashov and 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
[3] E. Navruzov and 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: 10.1109/IEMTRONICS55184.2022.9795729.
[4] 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.
[5] A. Kabulov, I. Normatov, E. Urunbaev and 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.
[6] A.Kabulov, I. Normatov, A.Seytov and 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.
[7] 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. doi:10.1088/1742-6596/1260/10/102006
[8] Kabulov, A.V., Normatov, I.H. Ashurov A.O. (2019). Computational methods of minimization of multiple functions. Journal of Physics: Conference Series, 1260(10), 10200. doi:10.1088/1742-6596/1260/10/102007
[9] Yablonskii S.V. Vvedenie v diskretnuyumatematiku: Ucheb. posobiedlyavuzov. -2e izd., pererab. idop. -M.:Nauka. Glavnayaredaksiyafiziko-matematicheskoy literature, -384 s.
[10] Djukova, E.V., Zhuravlev, Y.I. Monotone Dualization Problem and Its Generalizations: Asymptotic Estimates of the Number of Solutions. Comput. Math. and Math. Phys. 58, 2064–2077 (2018). https://doi.org/10.1134/S0965542518120102
[11] Leont’ev, V.K. Symmetric boolean polynomials. Comput. Math. and Math. Phys. 50, 1447–1458 (2010). https://doi.org/10.1134/S0965542510080142
[12] Nisan, N. and Szegedy, M. (1991). On the Degree of Boolean Functions as Real Polynomials, in preparation.
[13] RamamohanPaturi. 1992. On the degree of polynomials that approximate symmetric Boolean functions (preliminary version). In Proceedings of the twenty-fourth annual ACM symposium on Theory of Computing (STOC ’92). Association for Computing Machinery, New York, NY, USA, 468–474. https://doi.org/10.1145/129712.129758.
[14] Gu J., Purdom P., Franco J., Wah B.W. Algorithms for the satisfiability (SAT) problem:A Survey // DIMACS Series in Discrete Mathematics and Theoretical Computer Science. 1997.Vol. 35. P. 19–152.
[15] Goldberg E., Novikov Y. BerkMin: A Fast and Robust SAT Solver // Automation andTest in Europe (DATE). 2002. P. 142–149.
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Как цитировать
Bayzhumanov, A. A. (2023). Екiншi дәрежелi сызықты емес теңдеулер жүйесiнiң арнайы кластарын шешудiң оңтайлы әдiсi. Қазұу Хабаршысы. Математика, механика, информатика сериясы, 118(2), 11–20. https://doi.org/10.26577/JMMCS.2023.v118.i2.02
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