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In this paper we present algorithms for approximate FSM traversal based on state space decomposition. The original FSM is partitioned in sub-machines, and each of them is traversed separately; the result is an over-estimation of the set of reachable states. Several traversal strategies are discussed. Good partitioning is important for the performance of the traversal techniques; a method to heuristically find an appropriate decomposition, based on the exploration of the FSM latch connection graph, is proposed. Applications of the approximate traversal methods to sequential optimization and behavioral verification of FSM's are described; experimental results for such applications, together with data concerning pure traversal, are reported.