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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Kazan Federal University
2020-09-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
| Subjects: | |
| 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. |
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| ISSN: | 2541-7746 2500-2198 |