RUS  ENG
Полная версия
ЖУРНАЛЫ // Сибирские электронные математические известия // Архив

Сиб. электрон. матем. изв., 2023, том 20, выпуск 2, страницы 1499–1518 (Mi semr1656)

Дискретная математика и математическая кибернетика

О строении одного класса совершенных $\Pi$-разбиений

К. Л. Рычков

Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Аннотация: The concept of $\Pi$-partition is an analogue of the concept of normalized formula (a formula in the basis $\{\vee,\wedge,^-\}$ in which negations are possible only over variables) and concept of $\Pi$-schema, just as these last two concepts are analogues of each other. At its core, a $\Pi$-partition is a kind of "imprint" of a formula in the Boolean function calculated by this formula and is considered as a representation of this formula. In order to describe the class of minimal normalized formulas that calculate linear Boolean functions, the structure of the $\Pi$-partitions representing these formulas has been clarified.

Ключевые слова: boolean functions, $\pi$-schemes, normalized formulas, lower bounds on the complexity, formula representation.

УДК: 519.714

MSC: 03D15

Поступила 26 ноября 2023 г., опубликована 22 декабря 2023 г.

DOI: doi.org/10.33048/semi.2023.20.093



© МИАН, 2024