Efficient manipulation algorithms for linearly transformed BDDs

Wolfgang Günther, R. Drechsler
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引用次数: 15

Abstract

Binary decision diagrams (BDDs) are the state-of-the-art data structure in VLSI CAD, but, due to their ordering restriction, only exponential-sized BDDs exist for many functions of practical relevance. Linear transformations (LTs) have been proposed as a new concept to minimize the size of BDDs, and it is known that, in some cases, even an exponential reduction can be obtained. In addition to a small representation, the efficient manipulation of a data structure is also important. In this paper, we present polynomial-time manipulation algorithms that can be used for linearly transformed BDDs (LT-BDDs) analogously to BDDs. For some operations, like synthesis algorithms based on ITE (if-then-else), it turns out that the techniques known from BDDs can be directly transferred, while for other operations, like quantification and cofactor computation, completely different algorithms have to be used. Experimental results are given to show the efficiency of the approach.
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线性变换bdd的有效操作算法
二进制决策图(bdd)是VLSI CAD中最先进的数据结构,但是,由于它们的顺序限制,只有指数大小的bdd才存在于许多实际相关的功能中。线性变换(LTs)作为最小化bdd大小的新概念已经被提出,并且已知,在某些情况下,甚至可以获得指数缩小。除了较小的表示之外,数据结构的有效操作也很重要。在本文中,我们提出了一种多项式时间操作算法,可用于类似于bdd的线性变换bdd (lt - bdd)。对于某些操作,如基于ITE (if-then-else)的合成算法,事实证明,从bdd中已知的技术可以直接转移,而对于其他操作,如量化和辅因子计算,则必须使用完全不同的算法。实验结果表明了该方法的有效性。
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