Several conditions for uniformity of a finite system of many-valued logic
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 3, pp. 123-131
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We consider the relation between depth and complexity of many-valued logic functions over finite functional systems. The functional system $A$ is called quasi-uniform if there exist constants $c$ and $d$ such that for an arbitrary function $f$ from the closure of $A$ the inequality $D_A(f)\leq c\log_2^2L_A(f)+d$ holds, where $D_A(f)$ and $L_A(f)$ are the depth and the complexity of realization of the function $f$ by formulas over the finite system $A$. In this paper we provide some conditions for the quasi-uniformity of systems of functions of many-valued logic that take two values $0$ and $1$ and are monotone on the partially ordered set $\{0,\ldots,k-1\}$, where $1>0$ and all other elements are incomparable.
Keywords:
many-valued logic, depth, complexity, uniformity, parallelizing.
@article{UZKU_2014_156_3_a12,
author = {P. B. Tarasov},
title = {Several conditions for uniformity of a~finite system of many-valued logic},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {123--131},
publisher = {mathdoc},
volume = {156},
number = {3},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a12/}
}
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%0 Journal Article %A P. B. Tarasov %T Several conditions for uniformity of a finite system of many-valued logic %J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki %D 2014 %P 123-131 %V 156 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a12/ %G ru %F UZKU_2014_156_3_a12
P. B. Tarasov. Several conditions for uniformity of a finite system of many-valued logic. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 3, pp. 123-131. http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a12/