It has recently been shown that local search is surprisingly good at nding satisfying assignments for certain classes of CNF formulas 24]. In this paper we demonstrate that the power of local search for satis ability testing can be further enhanced by employing a new strategy, called \mixed random walk", for escaping from local minima. We present experimental results showing how this strategy allows us to handle formulas that are substantially larger than those that can be solved with basic local search. We also present a detailed comparison of our random walk strategy with simulated annealing. Our results show that mixed random walk is the superior strategy on several classes of computationally di cult problem instances. Finally, we present results demonstrating the e ectiveness of local search with walk for solving circuit synthesis and diagnosis problems.
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