Abstract
The original algorithm for the SAT problem, Variable Elimination Resolution (VER/DP) has exponential space complexity. To tackle that, the backtracking-based DPLL procedure [2] is used in SAT solvers. We present a combination of two techniques: we use NiVER, a special case of VER, to eliminate some variables in a preprocessing step, and then solve the simplified problem using a DPLL SAT solver. NiVER is a strictly formula size not increasing resolution based preprocessor. In the experiments, NiVER resulted in up to 74% decrease in N (Number of variables), 58% decrease in K (Number of clauses) and 46% decrease in L (Literal count). In many real-life instances, we observed that most of the resolvents for several variables are tautologies. Such variables are removed by NiVER. Hence, despite its simplicity, NiVER does result in easier instances. In case NiVER removable variables are not present, due to very low overhead, the cost of NiVER is insignificant. Empirical results using the state-of-the-art SAT solvers show the usefulness of NiVER. Some instances cannot be solved without NiVER preprocessing. NiVER consistently performs well and hence, can be incorporated into all general purpose SAT solvers.
Research reported supported in part by EPSRC(UK). Most of this work was done when the first author was working at University of Bristol.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Davis, M., Putnam, H.: A Computing procedure for quantification theory. J. of the ACMÂ 7 (1960)
Davis, M., et al.: A machine program for theorem proving. Comm. of ACMÂ 5(7) (1962)
Bachhus, F., Winter, J.: Effective preprocessing with Hyper-Resolution and Equality Reduction. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 341–355. Springer, Heidelberg (2004)
Brafman, R.I.: A simplifier for propositional formulas with many binary clauses. In: IJCAI 2001, pp. 515–522 (2001)
Goldberg, E., Novikov, Y.: BerkMin: a Fast and Robust SAT-Solver. In: Proc. of DATE 2002, pp. 142–149 (2002)
Moskewicz, M., et al.: Chaff: Engineering an efficient SAT solver. In: Proc. of DAC 2001 (2001)
Franco, J.: Elimination of infrequent variables improves average case performance of satisfiability algorithms. SIAM Journal on Computing 20, 1119–1127 (1991)
Van Gelder, A.: Combining preorder and postorder resolution in a satisfiability solver. In: Kautz, H., Selman, B. (eds.) Electronic Notes of SAT 2001. Elsevier, Amsterdam (2001)
Hoos, H., Stützle, T.: SATLIB: An Online Resource for Research on SAT. In: Gent, I.P., Maaren, H.v., Walsh, T. (eds.) SAT 2000, pp. 283–292 (2000), www.satlib.org
IBM Formal Verification Benchmarks Library, http://www.haifa.il.ibm.com/projects/verification/RB_Homepage/bmcbenchmarks.html
Ryan, L.: Siege SAT Solver, http://www.cs.sfu.ca/~loryan/personal/
NiVER SAT Preprocessor, http://www.itu.dk/people/sathi/niver.html
Hirsch, E.D.: New Worst-Case Upper Bounds for SAT. J. of Automated Reasoning 24, 397–420 (2000)
Biere, A.: BMC, http://www-2.cs.cmu.edu/~modelcheck/bmc.html
Velev, M.N.: Microprocessor Benchmarks, http://www.ece.cmu.edu/~mvelev/sat_benchmarks.html
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Subbarayan, S., Pradhan, D.K. (2005). NiVER: Non-increasing Variable Elimination Resolution for Preprocessing SAT Instances. In: Hoos, H.H., Mitchell, D.G. (eds) Theory and Applications of Satisfiability Testing. SAT 2004. Lecture Notes in Computer Science, vol 3542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11527695_22
Download citation
DOI: https://doi.org/10.1007/11527695_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27829-0
Online ISBN: 978-3-540-31580-3
eBook Packages: Computer ScienceComputer Science (R0)