K*BMDs: a new data structure for verification

Recently, two new dates structures have been proposed in the area of Computer Aided Design (CAD), i.e. Ordered Kronecker Functional Decision Diagrams (OKFDDs) and Multiplicative Binary Moment Diagrams (*BMDs). OKFDDs are the most general ordered data structure for representing Boolean functions at the bit-level. *BMDs are especially applicable to integer valued functions. In this paper we propose a new data structure, called Kronecker Multiplicative BMDs (K*BMDs), that is a generalization of OKFDDs to the word-level. Using K*BMDs it is possible to represent functions efficiently, that have a good word-level description, since K*BMDs are a generalization of *BMDs. On the other hand they are also applicable to verification problems at the bit-level. We present experimental results to demonstrate the efficiency of our approach including a comparison of K*BMDs to several other data structures, like EVBDD, OKFDDs and *BMDs. Additionally, experiments on verification of fast multipliers, i.e. multipliers with worst case running time O(log(n)), are reported.

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