Bounds of non-monotone complexity for the multi-valued logic functions

The non-monotone complexity of realization of k-valued logic functions by circuits in a special basis was investigated. The basis consists of elements of two types: the first type comprises all monotone functions (with respect to the order 0 < 1 < 2 <···< k−1 ) with zero weight; the seco...

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Bibliographic Details
Main Authors: V.V. Kochergin, A.V. Mikhailovich
Format: Article
Language:English
Published: Kazan Federal University 2020-09-01
Series:Учёные записки Казанского университета: Серия Физико-математические науки
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Online Access:https://kpfu.ru/uz-eng-phm-2020-3-6.html
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Summary:The non-monotone complexity of realization of k-valued logic functions by circuits in a special basis was investigated. The basis consists of elements of two types: the first type comprises all monotone functions (with respect to the order 0 < 1 < 2 <···< k−1 ) with zero weight; the second type includes non-monotone elements with unit weight, the non-empty set of which is finite. The upper and lower bounds of non-monotone complexity (the minimum number of non-monotone elements) for an arbitrary k-valued logic function were established. The difference between the upper and lower bounds does not exceed a universal constant. The difference between the best upper and lower bounds known before is a constant that depends on the basis. The range of values for these constants is infinite.
ISSN:2541-7746
2500-2198