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Approximate reachability techniques trade off accuracy with the capacity to deal with bigger designs. Cho et al [3] proposed approximate FSM traversal algorithms over a partition of the set of state bits. In this paper we generalize it by allowing projections onto a collection of nondisjoint subsets of the state variables. We establish the advantage of having overlapping projections and present a new multiple constrain function for BDDs, to compute efficiently the approximate image during symbolic forward propagation using overlapping projections. We demonstrate the effectiveness of this new algorithm by applying it to several control modules from the I/O unit in the Stanford FLASH Multiprocessor. We also present our results on the larger ISCAS 89 benchmarks.

Approximate reachability techniques trade off accuracy for the capacity to deal with bigger desigw. In this paper, we extend the idea of approximations using overlapping projection to symbolic backward reachability. Thti is combined with a previous method of computing ouerapprom.mate forward reachable state sets using overlapping projections. The algom"thmcomputes a superset of the set of states that lie on a path from the initial state to a state that violates a specified invan.ant property. If this set h empty, there ti no possibility of violating the invan.ant. If this set is non-empty, it may be possible to prove the existence of such a path by searching for a counter-example. A simple heuristic is given, which seems to work well in practice, for generating a counter-example path from this appron.mation. JVe evaluate these new algom.thms by applying them to several control modules porn the I/O unit in the Stanford FLASH J!ultiprocessor.

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