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О характеристическом свойстве одного класса нормализованных формул, реализующих линейные булевы функции Full article

Journal Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304
Output data Year: 2024, Volume: 21, Number: 2, Pages: 1522-1548 Pages count : 27 DOI: 10.33048/semi.2024.21.097
Tags boolean functions, π-circuits, normalized formulas, lower bounds on complexity, formula representations, Π-partitions.
Authors Рычков К.Л. 1
Affiliations
1 Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0017

Abstract: By means of a modi cation of the method proposed by S. V. Yablonsky for constructing an economical (hypothetically minimal) normalized formula (Π-circuit) that calculates a given linear Boolean function, a whole class of similar formulas was constructed the class of so-called optimal perfect normalized formulas. Presumably it is the class of all minimal normalized formulas that compute this function. To prove this conjecture, we consider extending this class to the class of perfect normalized formulas that also compute the same function. It is established that a normalized formula is perfect if and only if it has a perfect representation on the own rectangle of the speci ed function.
Cite: Рычков К.Л.
О характеристическом свойстве одного класса нормализованных формул, реализующих линейные булевы функции
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2024. Т.21. №2. С.1522-1548. DOI: 10.33048/semi.2024.21.097
Dates:
Submitted: Aug 27, 2024
Published print: Dec 31, 2024
Published online: Dec 31, 2024
Identifiers: No identifiers
Citing: Пока нет цитирований
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