A New Equivalence Relation of Logic Functions and Its Application in the Design of AND-OR-EXOR Networks(<Special Section>Discrete Mathematics and Its Applications)
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概要
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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・2^<n-5> (n≥6) products. This upper bound is smaller than 2^<n-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.
- 社団法人電子情報通信学会の論文
- 2007-05-01
著者
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SASAO Tsutomu
Department of Computer Science and Electronics, Kyushu Institute of Technology
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Debnath Debatosh
Department Of Computer Science And Engineering Oakland University
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Sasao Tsutomu
Department Of Computer Science And Electronics Kyushu Institute Of Technology
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Debnath Debatosh
Department Of Computer Science And Electronics Faculty Of Computer Science And Systems Engineering K
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