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- Thomas Hofmeister, Uwe Schöning, Rainer Schuler, Osamu Watanabe
- STACS
- 2002

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)

- Sven Baumer, Rainer Schuler
- SAT
- 2003

- Rainer Schuler
- J. Algorithms
- 2005

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)

- Hubert Hug, Rainer Schuler
- Bioinformatics
- 2001

MOTIVATION
We devise a computational model using protein-protein interactions.
RESULTS
Peptide-antibody interactions can be used to perform a large number of small logical operations in parallel. We show for example how a sequence of operations can be used to compare the number of occurrences of an element in two sets and how to estimate the number of… (More)

- Wolfgang Lindner, Rainer Schuler, Osamu Watanabe
- IEEE Conference on Computational Complexity
- 1998

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)

- Hubert Hug, Rainer Schuler
- DNA
- 2001

- Rainer Schuler, Tomoyuki Yamakami
- J. Comput. Syst. Sci.
- 1992

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)

- Vikraman Arvind, Rainer Schuler
- ISAAC
- 2003

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)

- Rainer Schuler, Tomoyuki Yamakami
- COCOON
- 1995

In this paper, we discuss the complexity and properties of the sets which are computable in polynomial-time on average. This study is motivated by Levin's question of whether all sets in NP are solvable in polynomial-time on average for every reasonable (i.e., polynomial-time computable) distribution on the instances. Let PP-comp denote the class of all… (More)

- Rainer Schuler, Osamu Watanabe
- Structure in Complexity Theory Conference
- 1995

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)