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We report results from large-scale experiments in satis-ability testing. As has been observed by others, testing the satissability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which(More)
We report results from large-scale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which(More)
Finding sets of hard instances of propositional satissability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case complexity, the threshold phenomenon, known lower bounds for(More)
Most CSP algorithms are based on refinements and extensions of backtracking, and employ one of two simple " branching schemes " : 2-way branching or d-way branching, for domain size d. The schemes are not equivalent, but little is known about their relative power. Here we compare them in terms of how efficiently they can refute an unsatisfi-able instance(More)
NP search and decision problems occur widely in AI, and a number of general-purpose methods for solving them have been developed. The dominant approaches include propo-sitional satisfiability (SAT), constraint satisfaction problems (CSP), and answer set programming (ASP). Here, we propose a declarative constraint programming framework which we believe(More)
A grounding of a formula φ over a given finite domain is a ground formula which is equivalent to φ on that domain. Very effective propositional solvers have made grounding-based methods for problem solving increasingly important, however for realistic problem domains and instances, the size of groundings is often problematic. A key technique in ground(More)