The RDQ, family practitioners and gastroenterologists have moderate and similar accuracy for diagnosis of GORD. Symptom response to a 2 week course of 40 mg of esomeprazole does not add diagnostic precision.

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Abstract.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 find a satisfying assignment. Papadimitriou [11] introduced this random approach and applied it to the case of 2-SAT, obtaining an expected O(n 2 ) time bound. The novelty here is to restart the algorithm after 3n unsuccessful steps of local search. The analysis shows that for any satisfiable k-CNF formula with n variables the expected number of repetitions until a satisfying assignment is found this way is (2 · (k − 1)/k) n . Thus, for 3-SAT the algorithm presented here has a complexity which is within a polynomial factor of ( 4 3 ) n . This is the fastest and also the simplest among those algorithms known up to date for 3-SAT achieving an o(2 n ) time bound. Also, the analysis is quite simple compared with other such algorithms considered before.Key Words. Satisfiability problem, NP-completeness. Preliminaries.The decision problem k-SAT consists of the set of satisfiable formulas in conjunctive normal form (CNF) where each clause has at most k literals (a literal being a variable or a negated variable). By n we denote the number of variables that occur in a given formula. For convenience we assume that in a k-SAT formula each clause has exactly k literals. This can be achieved by doubling some of the literals. The "naive algorithm" for k-SAT which tries out all 2 n truth value assignments to the n variables has a complexity which is within a polynomial factor of 2 n . By the fact that k-SAT is NP-complete [2], [6] for every k ≥ 3, it would follow that P = NP if a polynomial-time algorithm could be devised for this problem (which seems very difficult if not impossible). However, it is still interesting and desirable for practical purposes to find algorithms which are better than the naive 2 n algorithm. A milestone paper in this respect is by Monien and Speckenmeyer [9] where a deterministic algorithm for k-SAT is presented. For 3-SAT their bound is 1.618 n . The best bounds so far have been obtained by a probabilistic algorithm (see [10]) which started in the paper [13] and was further improved by Paturi et al. in [12]. Their algorithm is based on a probabilistic version of the Davis-Putnam procedure. In the case of 3-SAT the bound given in [12] is 1.362 n . Here we present a different probabilistic algorithm for k-SAT based on local search that achieves the bound (2(k − 1)/k) n . In the case of 3-SAT the complexity is therefore ( 4 3 ) n . This is the fastest known algorithm for 3-SAT up to date (but see the remark at the 616U. Schöning end of this paper). Also, the algorithm and its analysis is quite simple compared with its predecessors. Comparing our bounds in the cases k ≥ 4, these bounds are slightly beaten by the probabilistic algorithm deve...