Tighter Hard Instances for PPSZ
نویسندگان
چکیده
We construct uniquely satisfiable k-CNF formulas that are hard for the algorithm PPSZ. Firstly, we construct graph-instances on which “weak PPSZ” has savings of at most (2 + ǫ)/k; the saving of an algorithm on an input formula with n variables is the largest γ such that the algorithm succeeds (i.e. finds a satisfying assignment) with probability at least 2. Since PPSZ (both weak and strong) is known to have savings of at least π +o(1) 6k , this is optimal up to the constant factor. In particular, for k = 3, our upper bound is 2, which is fairly close to the lower bound 2 of Hertli [SIAM J. Comput.’14]. We also construct instances based on linear systems over F2 for which strong PPSZ has savings of at most O (
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