TY - JOUR

T1 - Minimizing ESCT forms for two-variable multiple-valued input binary output functions

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 .

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.

KW - AND-EXOR expression

KW - Boolean matrix

KW - Minimization

KW - Multiple-valued logic function

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U2 - 10.1016/j.dam.2013.12.023

DO - 10.1016/j.dam.2013.12.023

M3 - Article

AN - SCOPUS:84895926126

SN - 0166-218X

VL - 169

SP - 186

EP - 194

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -