Rainer Schuler

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In [?], Schöning proposed a simple yet efficient randomized algorithm for solving the k-SAT problem. In the case of 3-SAT, the algorithm has an expected running time of poly(n) · (4/3) n = O(1.3334 n) 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(More)
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+log m)) , 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(More)
We consider the resource bounded measure of polynomial-time learnable subclasses of polynomial-size circuits. We show that if EXP 6 = 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)
Levin introduced an average-case complexity measure, based on a notion of \polynomial on-average," and deened \average-case polynomial-time m a n y-one reducibility" among randomized decision problems. We generalize his notions of average-case complexity classes, Random-NP and Average-P. Ben-David et al. use the notation of hC F ito denote the set of(More)
Toluene can have striking acute behavioral effects and is subject to abuse by inhalation. To determine if its actions resemble those of drugs used in the treatment of anxiety ("anxiolytics"), two sets of experiments were undertaken. Inasmuch as prevention of pentylenetetrazol-induced convulsions is an identifying property of this class of agents, we first(More)
We first give añ O(2 n/3) 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 añ O(2 n/3 n d) quantum algorithm. For d = o(n/ log n) this running time is bounded by˜O(2 n(1/3+ǫ)) for every ǫ > 0 and in particular it is better than the˜O(2 n/2) upper(More)