# A New Method for Solving Hard Satisfiability Problems

@inproceedings{Selman1992ANM, title={A New Method for Solving Hard Satisfiability Problems}, author={Bart Selman and Hector J. Levesque and David G. Mitchell}, booktitle={AAAI}, year={1992} }

We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approaches such as the Davis-Putnam procedure or resolution. We also show that GSAT can solve structured satisfiability problems quickly. In particular, we solve encodings of graph coloring problems, N…

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## References

SHOWING 1-10 OF 39 REFERENCES

Efficient local search for very large-scale satisfiability problems

- Computer ScienceSGAR
- 1992

In this correspondence, the results of applying local search techniques to solve the satisfiability problem are reported.

Solving Large-Scale Constraint-Satisfaction and Scheduling Problems Using a Heuristic Repair Method

- Computer ScienceAAAI
- 1990

A theoretical analysis is presented to explain why the heuristic method for solving large-scale constraint satisfaction and scheduling problems works so well on certain types of problems and to predict when it is likely to be most effective.

Probabilistic analysis of the Davis Putnam procedure for solving the satisfiability problem

- Computer Science, MathematicsDiscret. Appl. Math.
- 1983

A ‘reasonable’ family of instance distributions F is presented and it is shown that for each distribution in F a variant of the Davis Putnam Procedure without the pure literal rule requires exponential time with probability 1.

Hard and Easy Distributions of SAT Problems

- Computer ScienceAAAI
- 1992

It is shown 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 satisfiability testing is quite difficult.

The complexity of theorem-proving procedures

- Computer Science, MathematicsSTOC
- 1971

It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a…

Resolution vs. cutting plane solution of inference problems: Some computational experience

- Mathematics
- 1988

Resolvents in the propositional calculus correspond to certain cutting planes in integer programming models of inference problems. We compare the performance of a rudimentary cutting plane algorithm…

Computers and Intractability: A Guide to the Theory of NP-Completeness

- Computer Science, Mathematics
- 1978

Horn formulae play a prominent role in artificial intelligence and logic programming. In this paper we investigate the problem of optimal compression of propositional Horn production rule knowledge…

A continuous approach to inductive inference

- Mathematics, Computer ScienceMath. Program.
- 1992

This paper introduces a new variant of this algorithm, where the Riemannian metric used for defining the search region is dynamically modified, and gives a method to synthesize a Boolean function that describes the sample.

On the Greedy Algorithm for Satisfiability

- Mathematics, Computer ScienceInf. Process. Lett.
- 1992

Abstract We show that for the vast majority of satisfiable 3CNF formulae, the local search heuristic that starts at a random truth assignment and repeatedly flips the variable that improves the…

Optimization by Simulated Annealing: An Experimental Evaluation; Part II, Graph Coloring and Number Partitioning

- Mathematics, Computer ScienceOper. Res.
- 1991

This is the second in a series of three papers that empirically examine the competitiveness of simulated annealing in certain well-studied domains of combinatorial optimization. Simulated annealing…