Abstract
CNF propositional satisfiability (SAT) is a special kind of the more general Constraint Satisfaction Problem (CSP). While lookback techniques appear to be of little use to solve hard random SAT problems, it is supposed that they are necessary to solve hard structured SAT problems. In this paper, we propose a very simple DPL procedure called Satz which only employs some look-ahead techniques: a variable ordering heuristic, a forward consistency checking (Unit Propagation) and a limited resolution before the search, where the heuristic is itself based on unit propagation. Satz is favorably compared on random 3-SAT problems with three DPL procedures among the best in the literature for these problems. Furthermore on a great number of problems in 4 well known SAT benchmarks Satz reaches or outspeeds the performance of three other DPL procedures among the best in the literature for structured SAT problems. The comparative results suggest that a suitable exploitation of look-ahead techniques, while very simple and efficient for random SAT problems, may allow to do without sophisticated look-back techniques in a DPL procedure.
Preview
Unable to display preview. Download preview PDF.
References
Bayardo Jr. R.J., Schrag R.C., Using CSP Look-Back Techniques to Solve Exceptionally Hard SAT Instances, Proceedings of the Second International Conference on Principles and Practice of Constraint Programming (CP96), Cambridge, Massachusetts, USA, August 1996.
Bayardo Jr. R.J., Schrag R.C., Using CSP Look-Back Techniques to Solve Real-World SAT Instances, to appear in proceedings of AAAI-97, Providence, Rhode Island, July 1997.
Billionnet A., Sutter A., An efficient algorithm for 3-satisfiability problem, Operations Research Letters, 12:29–36, July 1992.
Cook S.A., The Complexity of Theorem Proving Procedures, Proceedings of 3rd ACM Symp. on Theory of Computing, Ohio, 1971, pp. 151–158.
Crawford J.M., Auton L.D., Experimental results on the Crossover point in Random 3-SAT,Artificial Intelligence, No. 81, 1996.
Davis M., Logemann G., Loveland D., A machine program for theorem proving, Commun. ACM 5, 1962, pp. 394–397.
Dubois O., Andre P., Boufkhad Y., Carlier J., SAT versus UNSAT. Second DIMACS Implementation Challenge, D. S. Johnson and M. A. Trick (eds.), 1993.
Freeman J.W., Improvements to propositional satisfiability search algorithms, Ph.D. Thesis, Department of computer and Information science, University of Pennsylvania, Philadelphia, PA, 1995.
Gloess P.Y., U-Log, a Unified Object Logic, Revue d'intelligence artificielle, Vol. 5, No. 3, 1991, pp. 33–66.
Hooker J.N., Vinay V., Branching rules for satisfiability, Journal of Automated Reasoning, 15:359–383, 1995.
Jeroslow R., Wang J., Solving propositional satisfiability problems, Annals of Mathematics and AI 1, 1990, pp. 167–187.
Kim S., Zhang H., ModGen: Theorem proving by model generation, Proceedings of the 12th National Conference on Artificial Intelligence (AAAI-94), 1994, pp. 162–167.
Li C.M., Exploiting yet more the power of unit clause propagation to solve 3-SAT problem, Proceedings of the ECAI'96 Workshop on Advances in Propositional Deduction, Budapest, Hungary, August 1996, pp. 11–16.
Li C.M., Anbulagan, Heuristics Based on Unit Propagation for Satisfiability Problems, to appear in Proceedings of IJCAI'97, Nagoya, Japan, August 1997.
Mitchell D., Selman B., Levesque H., Hard and Easy Distributions of SAT Problems, Proceedings of the 10th National Conference on Artificial Intelligence (AAAI-92), San Jose, CA, July 1992, pp. 459–465.
Pretolani D., Satisfiability and hypergraphs, Ph.D. Thesis, Dipartimento di Informatica, Università di Pisa, 1993.
Silva J. P. M., Sakallah K. A., Conflict Analysis in Search Algorithms for Propositional Satisfiability, Proceedings of the International Conference on Tools with Artificial Intelligence, November 1996.
Stephan P. R., Brayton R. K., Sangiovanni-Vincentelli A. L., Combinational Test Generation Using Satisfiability, Memorandum No. UCB/ERL M92/112, EECS Department, University of California at Berkeley, October 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, C.M., Anbulagan (1997). Look-ahead versus look-back for satisfiability problems. In: Smolka, G. (eds) Principles and Practice of Constraint Programming-CP97. CP 1997. Lecture Notes in Computer Science, vol 1330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017450
Download citation
DOI: https://doi.org/10.1007/BFb0017450
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63753-0
Online ISBN: 978-3-540-69642-1
eBook Packages: Springer Book Archive