Rainer Schuler

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We consider the satisfiability problem on Boolean formulas in conjunctive normal form. We show that a satisfying assignment of a formula can be found in polynomial time with a success probability of 2−n(1−1/(1+logm)), where n and m are the number of variables and the number of clauses of the formula, respectively. If the number of clauses of the formulas is(More)
In [?], Schöning proposed a simple yet efficient randomized algorithm for solving the kSAT problem. In the case of 3-SAT, the algorithm has an expected running time of poly(n) · (4/3) = O(1.3334) when given a formula F on n variables. This was the up to now best running time known for an algorithm solving 3-SAT. In this paper, we describe an algorithm which(More)
We consider the resource-bounded measure of polynomial-time learnable subclasses of polynomial-size circuits. We show that if EXP ≠ MA, then every PAC-learnable subclass of P/poly has EXP-measure zero. We introduce a nonuniformly computable variant of resource-bounded measure and show that, for every fixed polynomial q , any polynomial-time learnable(More)
We first give an Õ(2) quantum algorithm for the 0-1 Knapsack problem with n variables. More generally, for 0-1 Integer Linear Programs with n variables and d inequalities we give an Õ(2n) quantum algorithm. For d = o(n/ logn) this running time is bounded by Õ(2) for every ǫ > 0 and in particular it is better than the Õ(2) upper bound for general quantum(More)
For the worst case complexity measure if P NP then P OptP i e all NP optimization problems are polynomial time solvable On the other hand it is not clear whether a similar relation holds when considering average case complexity We investigate the relationship between the complexity of NP decision problems and that of NP optimization problems under(More)