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- Uwe Schöning
- FOCS
- 1999

We present a simple probabilistic algorithm for solving k-SAT, and more generally, for solving constraint satisfaction problems (CSP). The algorithm follows a simple local-search paradigm (cf. [9]): randomly guess an initial assignment and then, guided by those clauses (constraints) that are not satisfied, by successively choosing a random literal from such… (More)

Local search is widely used for solving the propositional satisÿability problem. Papadim-itriou (1991) showed that randomized local search solves 2-SAT in polynomial time. Recently, Sch oning (1999) proved that a close algorithm for k-SAT takes time (2 − 2=k) n up to a polynomial factor. This is the best known worst-case upper bound for randomized 3-SAT… (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)

A simple probabilistic algorithm for solving the NP-complete problem k-SAT is reconsidered. This algorithm follows a well-known local-search paradigm: randomly guess an initial assignment and then, guided by those clauses that are not satisfied, by successively choosing a random literal from such a clause and changing the corresponding truth value, try to… (More)

We introduce a new class of functions, called span functions which count the different output values that occur at the leaves of the computation tree associated with a nondeterministic polynomial time Turing machine transducer. This function class has natural complete problems; it is placed between Valiant's function classes # P and =~ NP, and contains both… (More)

We introduce a measure for the computational complexity of mdiwdual instances of a decision problem and study some of Its properties. The instance complexity of a string ~ with respect to a set A and time bound t, ict(x : A). is defined as the size of the smallest special-case program for A that run> m time t,decides x correctly, and makes no mistakes on… (More)

We show that satisfiability of formulas in k-CNF can be decided deterministically in time close to (2k/(k + 1)) n , where n is the number of variables in the input formula. This is the best known worst-case upper bound for deterministic k-SAT algorithms. Our algorithm can be viewed as a derandomized version of Schöning's probabilistic algorithm presented in… (More)