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A New Equivalence Relation of Logic Functions and Its Application in the Design of AND-OR-EXOR Networks Debatosh DEBNATH Tsutomu SASAO Publication IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Vol.E90-A No.5 pp.932-940 Publication Date: 2007/05/01 Online ISSN: 1745-1337 DOI: 10.1093/ietfec/e90-a.5.932 Print ISSN: 0916-8508 Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications) Category: Keyword: three-level networks, AND-EXOR, NP-equivalence, coordinate representation, µ-equivalence, spectral method, logic minimization, Full Text: PDF(227.1KB)>>
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. | ||||||||||
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