This paper describes a new data structure, difference decision diagrams (DDDs)

Determining the time separation of events is a fundamental problem in the analysis, synthesis, and optimization of concurrent systems. Applications range from logic optimization of asynchronous digital circuits to evaluation of execution times of programs for real-time systems. We present an e cient algorithm to nd exact (tight) bounds on the separation time of events in an arbitrary process graph without conditional behavior. The algorithm is based on a functional decomposition technique that permits the implicit evaluation of an in nitely unfolded process graph.

Abstract.A state/event model is a concurrent version of Mealy machines used for describing embedded reactive systems. This paper introduces a technique that uses compositionality and dependency analysis to significantly improve the efficiency of symbolic model checking of state/event models. This technique makes possible automated verification of large industrial designs with the use of only modest resources (less than one hour on a standard PC for a model with 1421 concurrent machines). The results of the paper are being implemented in the next version of the commercial tool visualSTATE TM.

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This paper presents a new data structure called Boolean Expression Diagrams (BEDs) for representing and manipulating Boolean functions. BEDs are a generalization of Binary Decision Diagrams (BDDs) which can represent any Boolean circuit in linear space and still maintain many of the desirable properties of BDDs. Two algorithms are described for transforming a BED into a reduced ordered BDD. One closely mimics the BDD apply-operator while the other can exploit the structural information of the Boolean expression. The eficacy of the BED representation is demonstrated by verifying that the redundant and non-redundant versions of the ISCAS 85 benchmark circuits are identical. I n particular, it is verified that the two 16-bit multiplication circuits (c6288 and c6288nr) implement the same Boolean functions. Using BEDs, this verification problem is solved in less than a second, while using standard BDD techniques this problem is infeasible. BEDs are useful in applications where the end-result as a reduced ordered BDD is small, for example for tautology checking.

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