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Оценки немонотонной сложности функций многозначной логики
Ученые записки Казанского университета. Серия: Физико-математические науки. 2020. Т. 162. № 3. С. 311–321.
Kochergin V., Mikhailovich A.
The problem of the complexity of multi-valued logic functions realization by circuits
in a special basis is investigated. This kind of basis consists of elements of
two types. The first type of elements are monotone functions with zero weight.
The second type of elements are non-monotone elements with unit weight.
The non-empty set of elements of this type is finite.
In the paper the upper and the lower bounds for non-monotone complexity (the minimum number of non-monotone elements) for an arbitrary
multi-valued logic function are improved.
The difference between the upper bound and the lower bound does not exceed constant value.
The difference between the best upper and lower bounds known before is value which depends on basis and are
arbitrary large.
Borzykh D., Орлов Н. А., Экономический журнал Высшей школы экономики 2026 Т. 30 № 3 С. 457–486
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Inês G., Скороход С. Н., Matteo d. V. et al., Communications in Nonlinear Science and Numerical Simulation 2027 Vol. 164 P. 1–13
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A prototypical example of categorial grammars are those based on Lambek calculus, i.e. noncommutative intuitionistic linear logic. However, it has been noted that purely noncommutative operations are often not sufficient for modeling even very simple natural language phenomena. Therefore a number of alternative formalisms are considered in the literature: those using purely ``commutative'' linear logic ...
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Association for Computational Linguistics, 2026.
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Nikitiuk B., Lenev D., Pisarev V. et al., Journal of Colloid and Interface Science 2026 Vol. 718 Article 140444
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Deshchenya V., Nikolay D. Kondratyuk, Sivakova A. et al., Chemical Engineering Sciences 2027 Vol. 337 Article 124616
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Zubov A., Zubov A., Малявко, Я. et al., Computer Physics Communications 2025 Vol. 317 Article 109860
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Roman Prosvirnin, Suslov A., Aleksei Soldatov et al., Computation 2026 Vol. 14 No. 10 Article 261
Abstract
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Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Big Data and Cognitive Computing 2026 Vol. 10 No. 11 P. 1–52
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IEEE, 2026.
Proceedings of the X Scientific School "Dynamics of Complex Networks and their Applications"
(DCNA'2026) contain papers of reports of scientists and specialists in the field of intelligent technologies,
engineering education, research and design of complex networks.
DCNA'2026 was held from 10 to 12 September 2026 in Moscow, Russia, as a part of the International
Forum on Artificial Intelligence and ...
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Maddalena L., Yildiz B., Del Vecchio Blanco F. et al., Scientific data 2026 P. 1–20
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Flamarion M. V., Pelinovsky E., Wave Motion 2027 Vol. 148 Article 103867
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(mBBM) equation in a regime where a small parameter measures the departure from the classical
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Obsie E. Y., Zhan Y., Liu Y., Engineering Research Express 2026 Article 7
Maintaining plant health is crucial for crop quality, food security, and agricultural productivity. Although deep learning methods have shown strong potential for species, disease, and severity classification, most existing approaches tackle these tasks separately, failing to exploit shared representations and interdependencies among them. Furthermore, the variability of disease symptoms, such as subtle differences in size, ...
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Lev Pyatko, Sergey Aksenov, Regular and Chaotic Dynamics 2026 Vol. 31 No. 5 P. 794–813
In the circular restricted three-body problem, families of periodic and quasi-periodic orbits exist in the vicinity of the libration points and are of significant interest for practical applications. This work presents a neural network-based algorithm for orbit construction and station-keeping, applicable to both periodic and quasi-periodic orbits near collinear libration points. The method employs a ...
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Vorontsova T., М.: Академия, 2025.
The textbook has been prepared in accordance with the requirements of the federal state educational standards for secondary vocational education and is intended for studying the professional modules “Information Security in Information and Telecommunication Systems and Networks Using Software and Hardware‑Software Tools, Including Cryptographic Protection Tools” and “Information Security in Automated Systems Using Software and ...
Added: October 19, 2026
V. V. Kochergin, A. V. Mikhailovich, Mathematical notes 2025 Vol. 117 No. 4 P. 579–594
The exact value of the complexity of the circuit implementation of an arbitrary Boolean function in a certain basis consisting of negation and all monotone Boolean functions is found. The complexity of a function is defined as the least number of basis elements sufficient to construct a circuit implementation of this function. ...
Added: February 28, 2026
Kochergin V., Mikhailovich A., Математические заметки 2025 Т. 117 № 4 С. 523–542
The exact value of the complexity of the circuit implementation of an arbitrary Boolean function in a certain basis consisting of negation and all monotone Boolean functions is found. The complexity of a function is defined as the least number of basis elements sufficient to construct a circuit implementation of this function. ...
Added: April 8, 2025
Mikhailovich A., Kochergin V., М.: Физматлит, 2024.
Added: March 10, 2025
Kochergin V., Mikhailovich A., Mathematical notes 2023 Vol. 113 No. 5 P. 794–803
The problem of determining the nonmonotone complexity of the implementation ofk-valued logic functions by logic circuits in bases consisting of all monotone (with respect to thestandard order) functions and finitely many nonmonotone functions is investigated. In calculatingthe complexity measure under examination only those elements of the circuit which are assignednonmonotone basis functions are taken into ...
Added: November 19, 2023
Kochergin V., Mikhailovich A., В кн.: Материалы XIV Международного семинара "Дискретная математика и ее приложения" имени академика О.Б.Лупанова (Москва, МГУ, 20-25 июня 2022 г.).: М.: Институт прикладной математики им. М.В. Келдыша РАН, 2022. С. 76–79.
Установлена нижняя оценка немонотонной сложности функций многозначной логики, отличающающаяся от известной верхней оценки не более чем на абсолютную константу ...
Added: October 29, 2022