Minimization of 2-level AND/XOR Expressions using Ordered Kronecker Functional Decision Diagrams

We present two new classes of 2-level AND/XOR expressions: the class RKRO of Reduced Kronecker Expressions and the class GKRO of Generalized Kronecker Expressions. GKRO contains RKRO and KRO, the well-known class of Kronecker Expressions Sas93b] as a subclass. There is a close relation between RKROs, KROs, GKROs and Ordered Kro-necker Functional Decision Diagrams (OKFDDs) DST + 94], that together with eecient OKFDD algorithms can be utilized for (exact and heuristical) minimization of RKROs, KROs and GKROs. In this paper we concentrate on RKROs and KROs and propose several algorithms for their minimization. Experimental results are given to show the eeciency of our approach. For the rst time eecient minimized 2-level AND/XOR expressions are determined for benchmark functions with more than 100 variables. Furthermore, we compare our solutions to results obtainable for other classes of AND/XOR forms. In particular, RKROs are much smaller than FPRMs and also turn out to be superior to KROs. In many cases they are even as compact as GKROs.