Learn More
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)
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)
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. W e investigate the relationship between the complexity of NP decision problems and that of NP optimization problems(More)