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- 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+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)

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

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)

- Sven Baumer, Rainer Schuler
- SAT
- 2003

- Hubert Hug, Rainer Schuler
- DNA
- 2001

- 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)

- Johannes Köbler, Rainer Schuler
- Electronic Colloquium on Computational Complexity
- 1998

We use the assumption that all sets in NP (or other levels of the polynomial-time hierarchy) have eecient average-case algorithms to derive collapse consequences for MA, AM, and various subclasses of P/poly. As a further consequence we show for C 2 fP(PP); PSPACEg that C is not tractable in the average-case unless C = P.

- Wolfgang Lindner, Rainer Schuler, Osamu Watanabe
- Theory of Computing Systems
- 1998

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)

- Martin Mundhenk, Rainer Schuler
- J. Complexity
- 1991

A language A is considered to be random for a class C if for every language B in C the fraction of the strings where A and B coincide is approximately 1/2. We show that there exist languages in DSPACE(f(n)) which are random for the non-uniform class DSPACE(g(n))=h(n), where n, g(n) and h(n) are in o(f(n)). Non-uniform complexity classes were introduced by… (More)

- Vikraman Arvind, Rainer Schuler
- ISAAC
- 2003

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)

- 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 We investigate the relationship between the complexity of NP decision problems and that of NP optimization problems under… (More)