Clones of Self-Dual and Self-K-Al Functions in K-valued Logic
Pure and Applied Mathematics Journal
Volume 6, Issue 2, April 2017, Pages: 59-70
Received: Feb. 17, 2017; Accepted: Feb. 24, 2017; Published: Mar. 10, 2017
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Author
M. A. Malkov, Russian Research Center for Artificial Intelligence, Moscow, Russia
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Abstract
We give a classification of dual functions, they are m-al functions. We call a function m-al with respect to an operator if the operator lives any function unchanged after m times of using the operator. And 2 ≤ m ≤ k. Functions with different m have very different properties. We give theoretical results for clones of self-dual (m = 2) and self- -al (m = k) functions in k-valued logic at k ≤ 3. And we give numerical results for clones of self-dual and self-3-al functions in 3-valued logic. In particular, the inclusion graphs of clones of self-dual and of self-3-al functions are not a lattice.
Keywords
Discreate Mathematics, K-Valued Function Algebra, Selfdual Functions
To cite this article
M. A. Malkov, Clones of Self-Dual and Self-K-Al Functions in K-valued Logic, Pure and Applied Mathematics Journal. Vol. 6, No. 2, 2017, pp. 59-70. doi: 10.11648/j.pamj.20170602.11
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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