Application of Graph Theory Algorithms in Non-disjoint Functional Decomposition of Specific Boolean Functions

Functional decomposition is a technique that allows to minimize Boolean functions that cannot be optimally minimized using other methods, such as variable reduction and linear decomposition. A heuristic method for finding non-disjoint decomposition has been proposed lately. In this paper, we examine...

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Bibliographic Details
Published in:Journal of Telecommunications and Information Technology Vol. 3; no. 2020; pp. 67 - 74
Main Author: Mazurkiewicz, Tomasz
Format: Journal Article
Language:English
Published: Warsaw Instytut Lacznosci - Panstwowy Instytut Badawczy (National Institute of Telecommunications) 01.10.2020
National Institute of Telecommunications
Subjects:
Algebra
Algorithms
Boolean
Boolean algebra
Boolean functions
Decomposition
Field programmable gate arrays
functional decomposition
Functionals
Graph coloring
Graph theory
Heuristic
Heuristic methods
index generation functions
logic synthesis
non-disjoint decomposition
Variables
ISSN:1509-4553, 1899-8852
Online Access:Get full text
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Summary:Functional decomposition is a technique that allows to minimize Boolean functions that cannot be optimally minimized using other methods, such as variable reduction and linear decomposition. A heuristic method for finding non-disjoint decomposition has been proposed lately. In this paper, we examine how the usage of different graph theory techniques affects the computation time and the quality of the solution obtained. In total, six different approaches were analyzed. The results presented herein prove the advantages of the proposed approaches, showing that results obtained for standard benchmark M-out-of-20 functions are better than those presented in previous publication. Results obtained for randomly generated functions prove that time complexity and scalability are significantly better when using the heuristic graph coloring algorithm. However, quality of the solution is worse, in general.
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content type line 14
ISSN:1509-4553
1899-8852
DOI:10.26636/jtit.2020.142520