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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.
Trubochkina N. K., М.: Издательство «Юрайт», 2026.
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arays of texts.
Fоr students, graduate students and researchers studying methods
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This paper is expository and methodological in nature and is devoted to the development of E.I. Zolotarev’s ideas embedded in his approach to the proof of the quadratic reciprocity law (1872). We consider extensions of Zolotarev’s approach to abstract number rings presented in the work of A. Brunyate and P.L. Clark (2015), and to finite ...
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Ponomarenko A., / Series Computer Science "arxiv.org". 2025.
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Уилкокс П., Romanov A., М.: ДМК Пресс, 2025.
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Данная книга представляет собой учебник по теоретическим основам продвинутой
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время. В ней подробно описана унифицированная методология верификации
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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