IEICE TRANSACTIONS on Fundamentals
A New Equivalence Relation of Logic Functions and Its Application in the Design of AND-OR-EXOR Networks
Summary :
This paper presents a design method for AND-OR-EXOR three-level networks, where a single two-input exclusive-OR (EXOR) gate is used. The network realizes an EXOR of two sum-of-products expressions (EX-SOPs). The problem is to minimize the total number of products in the two sum-of-products expressions (SOPs). We introduce the notion of µ-equivalence of logic functions to develop exact minimization algorithms for EX-SOPs with up to five variables. We minimized all the NP-representative functions for up to five variables and showed that five-variable functions require 9 or fewer products in minimum EX-SOPs. For n-variable functions, minimum EX-SOPs require at most 9·2n-5 (n ≤ 6) products. This upper bound is smaller than 2n-1, which is the upper bound for SOPs. We also found that, for five-variable functions, on the average, minimum EX-SOPs require about 40% fewer literals than minimum SOPs.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E90-A No.5 pp.932-940
- Publication Date
- 2007/05/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e90-a.5.932
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
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Debatosh DEBNATH, Tsutomu SASAO, "A New Equivalence Relation of Logic Functions and Its Application in the Design of AND-OR-EXOR Networks" in IEICE TRANSACTIONS on Fundamentals,
vol. E90-A, no. 5, pp. 932-940, May 2007, doi: 10.1093/ietfec/e90-a.5.932.
Abstract: This paper presents a design method for AND-OR-EXOR three-level networks, where a single two-input exclusive-OR (EXOR) gate is used. The network realizes an EXOR of two sum-of-products expressions (EX-SOPs). The problem is to minimize the total number of products in the two sum-of-products expressions (SOPs). We introduce the notion of µ-equivalence of logic functions to develop exact minimization algorithms for EX-SOPs with up to five variables. We minimized all the NP-representative functions for up to five variables and showed that five-variable functions require 9 or fewer products in minimum EX-SOPs. For n-variable functions, minimum EX-SOPs require at most 9·2n-5 (n ≤ 6) products. This upper bound is smaller than 2n-1, which is the upper bound for SOPs. We also found that, for five-variable functions, on the average, minimum EX-SOPs require about 40% fewer literals than minimum SOPs.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e90-a.5.932/_p
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@ARTICLE{e90-a_5_932,
author={Debatosh DEBNATH, Tsutomu SASAO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A New Equivalence Relation of Logic Functions and Its Application in the Design of AND-OR-EXOR Networks},
year={2007},
volume={E90-A},
number={5},
pages={932-940},
abstract={This paper presents a design method for AND-OR-EXOR three-level networks, where a single two-input exclusive-OR (EXOR) gate is used. The network realizes an EXOR of two sum-of-products expressions (EX-SOPs). The problem is to minimize the total number of products in the two sum-of-products expressions (SOPs). We introduce the notion of µ-equivalence of logic functions to develop exact minimization algorithms for EX-SOPs with up to five variables. We minimized all the NP-representative functions for up to five variables and showed that five-variable functions require 9 or fewer products in minimum EX-SOPs. For n-variable functions, minimum EX-SOPs require at most 9·2n-5 (n ≤ 6) products. This upper bound is smaller than 2n-1, which is the upper bound for SOPs. We also found that, for five-variable functions, on the average, minimum EX-SOPs require about 40% fewer literals than minimum SOPs.},
keywords={},
doi={10.1093/ietfec/e90-a.5.932},
ISSN={1745-1337},
month={May},}
Copy
TY - JOUR
TI - A New Equivalence Relation of Logic Functions and Its Application in the Design of AND-OR-EXOR Networks
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 932
EP - 940
AU - Debatosh DEBNATH
AU - Tsutomu SASAO
PY - 2007
DO - 10.1093/ietfec/e90-a.5.932
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E90-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2007
AB - This paper presents a design method for AND-OR-EXOR three-level networks, where a single two-input exclusive-OR (EXOR) gate is used. The network realizes an EXOR of two sum-of-products expressions (EX-SOPs). The problem is to minimize the total number of products in the two sum-of-products expressions (SOPs). We introduce the notion of µ-equivalence of logic functions to develop exact minimization algorithms for EX-SOPs with up to five variables. We minimized all the NP-representative functions for up to five variables and showed that five-variable functions require 9 or fewer products in minimum EX-SOPs. For n-variable functions, minimum EX-SOPs require at most 9·2n-5 (n ≤ 6) products. This upper bound is smaller than 2n-1, which is the upper bound for SOPs. We also found that, for five-variable functions, on the average, minimum EX-SOPs require about 40% fewer literals than minimum SOPs.
ER -
English
