f(X) = α(g1(X1), g2(X2)). We call a bi-decomposition form optimal when the total number of variables in X1 and X2 is the smallest among all bi-decomposition forms of f. This meaning of optimal is adequate especially for the synthesis of LUT (Look-Up Table) networks where the number of function inputs is important for the implementation. In our method, we consider only two bi-decomposition forms; (g1 g2) and (g1 g2). We can easily find all the other types of bi-decomposition forms from the above two decomposition forms. Our method efficiently finds one of the existing optimal bi-decomposition forms based on a branch-and-bound algorithm. Moreover, our method can also decompose incompletely specified functions. Experimental results show that we can construct better networks by using optimal bi-decompositions than by using conventional decompositions." />


An Efficient Method for Finding an Optimal Bi-Decomposition

Shigeru YAMASHITA  Hiroshi SAWADA  Akira NAGOYA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E81-A   No.12   pp.2529-2537
Publication Date: 1998/12/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on VLSI Design and CAD Algorithms)
Category: Logic Synthesis
Keyword: 
functional decomposition,  bi-decomposition,  AND,  XOR,  look-up table,  

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Summary: 
This paper presents a new efficient method for finding an "optimal" bi-decomposition form of a logic function. A bi-decomposition form of a logic function is the form: f(X) = α(g1(X1), g2(X2)). We call a bi-decomposition form optimal when the total number of variables in X1 and X2 is the smallest among all bi-decomposition forms of f. This meaning of optimal is adequate especially for the synthesis of LUT (Look-Up Table) networks where the number of function inputs is important for the implementation. In our method, we consider only two bi-decomposition forms; (g1 g2) and (g1 g2). We can easily find all the other types of bi-decomposition forms from the above two decomposition forms. Our method efficiently finds one of the existing optimal bi-decomposition forms based on a branch-and-bound algorithm. Moreover, our method can also decompose incompletely specified functions. Experimental results show that we can construct better networks by using optimal bi-decompositions than by using conventional decompositions.