IEICE TRANSACTIONS on Fundamentals
A Faster Algorithm of Minimizing AND-EXOR Expressions
Summary :
It has been considered difficult to obtain the minimum AND-EXOR expression of a given function with six variables in a practical computing time. In this paper, a faster algorithm of minimizing AND-EXOR expressions is proposed. We believe that our algorithm can compute the minimum AND-EXOR expressions of any six-variable and some seven-variable functions practically. In this paper, we first present a naive algorithm that searches the space of expansions of a given n-variable function f for a minimum expression of f. The space of expansions are generated by using all combinations of (n-1)-variable product terms. Then, how to prune the branches in the search process and how to restrict the search space to obtain the minimum solutions are discussed as the key point of reduction of the computing time. Finally a faster algorithm is constructed by using the methods discussed. Experimental results to demonstrate the effectiveness of these methods are also presented.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E85-A No.12 pp.2708-2714
- Publication Date
- 2002/12/01
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section PAPER (Special Section on VLSI Design and CAD Algorithms)
- Category
- Logic Synthesis
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Keyword
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Takashi HIRAYAMA, Yasuaki NISHITANI, Toru SATO, "A Faster Algorithm of Minimizing AND-EXOR Expressions" in IEICE TRANSACTIONS on Fundamentals,
vol. E85-A, no. 12, pp. 2708-2714, December 2002, doi: .
Abstract: It has been considered difficult to obtain the minimum AND-EXOR expression of a given function with six variables in a practical computing time. In this paper, a faster algorithm of minimizing AND-EXOR expressions is proposed. We believe that our algorithm can compute the minimum AND-EXOR expressions of any six-variable and some seven-variable functions practically. In this paper, we first present a naive algorithm that searches the space of expansions of a given n-variable function f for a minimum expression of f. The space of expansions are generated by using all combinations of (n-1)-variable product terms. Then, how to prune the branches in the search process and how to restrict the search space to obtain the minimum solutions are discussed as the key point of reduction of the computing time. Finally a faster algorithm is constructed by using the methods discussed. Experimental results to demonstrate the effectiveness of these methods are also presented.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e85-a_12_2708/_p
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@ARTICLE{e85-a_12_2708,
author={Takashi HIRAYAMA, Yasuaki NISHITANI, Toru SATO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Faster Algorithm of Minimizing AND-EXOR Expressions},
year={2002},
volume={E85-A},
number={12},
pages={2708-2714},
abstract={It has been considered difficult to obtain the minimum AND-EXOR expression of a given function with six variables in a practical computing time. In this paper, a faster algorithm of minimizing AND-EXOR expressions is proposed. We believe that our algorithm can compute the minimum AND-EXOR expressions of any six-variable and some seven-variable functions practically. In this paper, we first present a naive algorithm that searches the space of expansions of a given n-variable function f for a minimum expression of f. The space of expansions are generated by using all combinations of (n-1)-variable product terms. Then, how to prune the branches in the search process and how to restrict the search space to obtain the minimum solutions are discussed as the key point of reduction of the computing time. Finally a faster algorithm is constructed by using the methods discussed. Experimental results to demonstrate the effectiveness of these methods are also presented.},
keywords={},
doi={},
ISSN={},
month={December},}
Copy
TY - JOUR
TI - A Faster Algorithm of Minimizing AND-EXOR Expressions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2708
EP - 2714
AU - Takashi HIRAYAMA
AU - Yasuaki NISHITANI
AU - Toru SATO
PY - 2002
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E85-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2002
AB - It has been considered difficult to obtain the minimum AND-EXOR expression of a given function with six variables in a practical computing time. In this paper, a faster algorithm of minimizing AND-EXOR expressions is proposed. We believe that our algorithm can compute the minimum AND-EXOR expressions of any six-variable and some seven-variable functions practically. In this paper, we first present a naive algorithm that searches the space of expansions of a given n-variable function f for a minimum expression of f. The space of expansions are generated by using all combinations of (n-1)-variable product terms. Then, how to prune the branches in the search process and how to restrict the search space to obtain the minimum solutions are discussed as the key point of reduction of the computing time. Finally a faster algorithm is constructed by using the methods discussed. Experimental results to demonstrate the effectiveness of these methods are also presented.
ER -
English
