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.
| DOI | 10.11648/j.pamj.20170602.11 |
| Published in | Pure and Applied Mathematics Journal (Volume 6, Issue 2, April 2017) |
| Page(s) | 59-70 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Discreate Mathematics, K-Valued Function Algebra, Selfdual Functions
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APA Style
M. A. Malkov. (2017). Clones of Self-Dual and Self-K-Al Functions in K-valued Logic. Pure and Applied Mathematics Journal, 6(2), 59-70. https://doi.org/10.11648/j.pamj.20170602.11
ACS Style
M. A. Malkov. Clones of Self-Dual and Self-K-Al Functions in K-valued Logic. Pure Appl. Math. J. 2017, 6(2), 59-70. doi: 10.11648/j.pamj.20170602.11
AMA Style
M. A. Malkov. Clones of Self-Dual and Self-K-Al Functions in K-valued Logic. Pure Appl Math J. 2017;6(2):59-70. doi: 10.11648/j.pamj.20170602.11
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Download@article{10.11648/j.pamj.20170602.11,
author = {M. A. Malkov},
title = {Clones of Self-Dual and Self-K-Al Functions in K-valued Logic},
journal = {Pure and Applied Mathematics Journal},
volume = {6},
number = {2},
pages = {59-70},
doi = {10.11648/j.pamj.20170602.11},
url = {https://doi.org/10.11648/j.pamj.20170602.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170602.11},
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.},
year = {2017}
}
TY - JOUR T1 - Clones of Self-Dual and Self-K-Al Functions in K-valued Logic AU - M. A. Malkov Y1 - 2017/03/10 PY - 2017 N1 - https://doi.org/10.11648/j.pamj.20170602.11 DO - 10.11648/j.pamj.20170602.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 59 EP - 70 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20170602.11 AB - 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. VL - 6 IS - 2 ER -
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