Heuristics to Minimize Multiple-Valued Decision Diagrams

Hafiz Md. HASAN BABU  Tsutomu SASAO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.12   pp.2498-2504
Publication Date: 2000/12/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on VLSI Design and CAD Algorithms)
Category: Logic Synthesis
binary decision diagram (BDD),  multiple-valued decision diagram (MDD),  multiple-output function,  multiple-valued logic,  FPGA design,  

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In this paper, we propose a method to minimize multiple-valued decision diagrams (MDDs) for multiple-output functions. We consider the following: (1) a heuristic for encoding the 2-valued inputs; and (2) a heuristic for ordering the multiple-valued input variables based on sampling, where each sample is a group of outputs. We first generate a 4-valued input 2-valued multiple-output function from the given 2-valued input 2-valued functions. Then, we construct an MDD for each sample and find a good variable ordering. Finally, we generate a variable ordering from the orderings of MDDs representing the samples, and minimize the entire MDDs. Experimental results show that the proposed method is much faster, and for many benchmark functions, it produces MDDs with fewer nodes than sifting. Especially, the proposed method generates much smaller MDDs in a short time for benchmark functions when several 2-valued input variables are grouped to form multiple-valued variables.