Minimizing ESCT forms for two-variable multiple-valued input binary output functions

Takaaki Mizuki; Daizo Mikami; Hideaki Sone

doi:10.1016/j.dam.2013.12.023

Minimizing ESCT forms for two-variable multiple-valued input binary output functions

Takaaki Mizuki, Daizo Mikami, Hideaki Sone

サイバーサイエンスセンター・研究開発部

研究成果: Article › 査読

1 被引用数 (Scopus)

抄録

As EXOR (Exclusive-OR) expansions of binary output functions, the ESOP (EXOR Sum of Products) form and its extension, the ESCT (EXOR Sum of Complex Terms) form, have been studied extensively in the literature. An efficient algorithm for minimizing ESOP forms is known for two-variable multiple-valued input functions. On the other hand, no ESCT minimization algorithm is known for such functions. In this paper, we give an efficient algorithm for minimizing ESCT forms of two-variable multiple-valued input functions, showing that the number of terms can be reduced by at most one.

本文言語	English
ページ（範囲）	186-194
ページ数	9
ジャーナル	Discrete Applied Mathematics
巻	169
DOI	https://doi.org/10.1016/j.dam.2013.12.023
出版ステータス	Published - 2014 5 31

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2013.12.023

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引用スタイル

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abstract = "As EXOR (Exclusive-OR) expansions of binary output functions, the ESOP (EXOR Sum of Products) form and its extension, the ESCT (EXOR Sum of Complex Terms) form, have been studied extensively in the literature. An efficient algorithm for minimizing ESOP forms is known for two-variable multiple-valued input functions. On the other hand, no ESCT minimization algorithm is known for such functions. In this paper, we give an efficient algorithm for minimizing ESCT forms of two-variable multiple-valued input functions, showing that the number of terms can be reduced by at most one.",

keywords = "AND-EXOR expression, Boolean matrix, Minimization, Multiple-valued logic function",

author = "Takaaki Mizuki and Daizo Mikami and Hideaki Sone",

note = "Funding Information: We thank Mr. Naoki Katagami for his valuable comments on the expression in Theorem 1 . We thank the associate editor and the anonymous referees whose comments helped us improve the presentation of the paper. This work was supported by JSPS KAKENHI Grant No. 23700007 . Copyright: Copyright 2014 Elsevier B.V., All rights reserved.",

year = "2014",

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AU - Mizuki, Takaaki

AU - Mikami, Daizo

AU - Sone, Hideaki

N1 - Funding Information: We thank Mr. Naoki Katagami for his valuable comments on the expression in Theorem 1 . We thank the associate editor and the anonymous referees whose comments helped us improve the presentation of the paper. This work was supported by JSPS KAKENHI Grant No. 23700007 . Copyright: Copyright 2014 Elsevier B.V., All rights reserved.

PY - 2014/5/31

Y1 - 2014/5/31

N2 - As EXOR (Exclusive-OR) expansions of binary output functions, the ESOP (EXOR Sum of Products) form and its extension, the ESCT (EXOR Sum of Complex Terms) form, have been studied extensively in the literature. An efficient algorithm for minimizing ESOP forms is known for two-variable multiple-valued input functions. On the other hand, no ESCT minimization algorithm is known for such functions. In this paper, we give an efficient algorithm for minimizing ESCT forms of two-variable multiple-valued input functions, showing that the number of terms can be reduced by at most one.

AB - As EXOR (Exclusive-OR) expansions of binary output functions, the ESOP (EXOR Sum of Products) form and its extension, the ESCT (EXOR Sum of Complex Terms) form, have been studied extensively in the literature. An efficient algorithm for minimizing ESOP forms is known for two-variable multiple-valued input functions. On the other hand, no ESCT minimization algorithm is known for such functions. In this paper, we give an efficient algorithm for minimizing ESCT forms of two-variable multiple-valued input functions, showing that the number of terms can be reduced by at most one.

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KW - Boolean matrix

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