Binary Decision Diagrams: Theory and Implementation by Rolf Drechsler

By Rolf Drechsler

For a person with a hammer the full global seems like a nail. in the final 10-13 years Binar·y choice Diagmms (BDDs) became the cutting-edge information constitution in VLSI CAD for illustration and ma­ nipulation of Boolean features. this present day, BDDs are favourite and meanwhile have additionally been built-in in advertisement instruments, specially within the quarter of verijication and synthesis. The curiosity in BDDs effects from the truth that the knowledge constitution is mostly approved as supplying a superb compromise among conciseness of illustration and potency of manipulation. With expanding variety of purposes, additionally in non CAD components, classical the way to deal with BDDs are being superior and new questions and difficulties evolve and feature to be solved. The booklet will help the reader who's now not acquainted with BDDs (or DDs normally) to get a short begin. nevertheless it's going to speak about numerous new points of BDDs, e.g. with recognize to minimization and implementation of a package deal. it will support humans operating with BDDs (in or academia) to maintain proficient approximately fresh advancements during this area.

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Extra resources for Binary Decision Diagrams: Theory and Implementation

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The above definition of EB-cln ,3 can naturally be reformulated in terms of a Ttransformation: EB-cl n ,3(X) = 1 Hf G(x) contains an odd number of subgraphs G(y) consisting only of a single 3-clique and n - 3 isolated nodes. e. EB-cl n ,3 = T(I-cl n ,3) EB-cl n ,3(X) = 1-cl n ,3(Y) , EB y-:;'x where 1-cl n ,3(x) = 1 iff G(x) consists only of a single 3-clique and n-3 isolated nodes. Comparing the representations by free DDs we show that 1-cl n ,3 can efficiently be described only using the BDD interpretation and EB-cln ,3 only with the pFDD interpretation.

Based on these concepts several theoretical studies have been performed. We summarize these results and thereby analyze the position of BDDs in the context of the "whole DD-world". 1 RELATION BETWEEN BDDS AND FDDS We start with some basic notations and definitions essential for the understanding of the following. e. BDDs and pFDDs. e. as BDD and pFDD, we use the following notation: 31 R. 1 1. If a DD G is interpreted as a BDD the function being represented is denoted as f3 DD . 2. If a DD G is interpreted as a pFDD the function being represented is denoted as f'ßFDD.

E. the "most important" variable is placed at the first position in the ordering and removed from the circuit. Subsequently, the weights are recomputed for the simplified circuit and the process is iterated until all variables are integrated in the ordering. The above ordering heuristics are based on DFS and thus compute an ordering very efficiently (in linear time or at least in quadratic time). There is no method that has turned out to be superior compared to the others. Each of them gives good results for some circuits.

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