Dynamic Scoring Functions with Variable Expressions: New SLS Methods for Solving SAT

  • Dave A. D. Tompkins
  • Holger H. Hoos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6175)


We introduce a new conceptual model for representing and designing Stochastic Local Search (SLS) algorithms for the propositional satisfiability problem (SAT). Our model can be seen as a generalization of existing variable weighting, scoring and selection schemes; it is based upon the concept of Variable Expressions (VEs), which use properties of variables in dynamic scoring functions. Algorithms in our model are constructed from conceptually separated components: variable filters, scoring functions (VEs), variable selection mechanisms and algorithm controllers. To explore the potential of our model we introduce the Design Architecture for Variable Expressions (DAVE), a software framework that allows users to specify arbitrarily complex algorithms at run-time. Using DAVE, we can easily specify rich design spaces of SLS algorithms and subsequently explore these using an automated algorithm configuration tool. We demonstrate that by following this approach, we can achieve significant improvements over previous state-of-the-art SLS-based SAT solvers on software verification benchmark instances from the literature.


Variable Expression Variable Property Search Step Stochastic Local Search Algorithm Controller 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Ansótegui, C., Bonet, M.L., Levy, J.: On the structure of industrial SAT instances. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 127–141. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  2. 2.
    Babić, D., Hu, A.J.: Calysto: Scalable and precise extended static checking. In: Proceedings of ICSE 2008, pp. 211–220 (2008)Google Scholar
  3. 3.
    Biere, A.: PicoSAT essentials. Journal on Satisfiability, Boolean Modeling and Computation 4, 75–97 (2008)zbMATHGoogle Scholar
  4. 4.
    Clarke, E., Kroening, D., Lerda, F.: A tool for checking ANSI-C programs. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 168–176. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Eén, N., Biere, A.: Effective preprocessing in SAT through variable and clause elimination. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 61–75. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Fukunaga, A.S.: Automated discovery of local search heuristics for satisfiability testing. Evolutionary Computation 16(1), 31–61 (2008)CrossRefGoogle Scholar
  7. 7.
    Gent, I.P., Walsh, T.: Towards an understanding of hill-climbing procedures for SAT. In: Proceedings of AAAI 1993, pp. 28–33 (1993)Google Scholar
  8. 8.
    Hoos, H.H.: Computer-aided design of high-performance algorithms. Tech. Rep. TR-2008-16, Department of Computer Science, University of British Columbia (2008)Google Scholar
  9. 9.
    Hoos, H.H., Stützle, T.: Stochastic Local Search: Foundations and Applications. Morgan Kaufmann, San Francisco (2005)zbMATHGoogle Scholar
  10. 10.
    Hutter, F., Babić, D., Hoos, H.H., Hu, A.J.: Boosting verification by automatic tuning of decision procedures. In: Proceedings of FMCAD 2007, pp. 27–34 (2007)Google Scholar
  11. 11.
    Hutter, F., Hoos, H.H., Leyton-Brown, K., Stützle, T.: ParamILS: An automatic algorithm configuration framework. Journal of Artificial Intelligence Research 36, 267–306 (2009)zbMATHGoogle Scholar
  12. 12.
    KhudaBukhsh, A.R., Xu, L., Hoos, H.H., Leyton-Brown, K.: SATenstein: Automatically building local search SAT solvers from components. In: IJCAI 2009, pp. 517–524 (2009)Google Scholar
  13. 13.
    Li, C.M., Huang, W.Q.: Diversification and determinism in local search for satisfiability. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 158–172. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    McAllester, D., Selman, B., Kautz, H.: Evidence for invariants in local search. In: Proceedings of AAAI 1997, pp. 321–326 (1997)Google Scholar
  15. 15.
    Prestwich, S.: Random walk with continuously smoothed variable weights. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 203–215. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  16. 16.
    Selman, B., Kautz, H.A., Cohen, B.: Noise strategies for improving local search. In: Proceedings of AAAI 1994, pp. 337–343 (1994)Google Scholar
  17. 17.
    Selman, B., Levesque, H., Mitchell, D.: A new method for solving hard satisfiability problems. In: Proceedings of AAAI 1992, pp. 459–465 (1992)Google Scholar
  18. 18.
    Tompkins, D.A.D., Hoos, H.H.: UBCSAT: An implementation and experimentation environment for SLS algorithms for SAT and MAX-SAT. In: Hoos, H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 306–320. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  19. 19.
  20. 20.
    Wei, W., Li, C.M., Zhang, H.: A switching criterion for intensification and diversification in local search for SAT. Journal on Satisfiability, Boolean Modeling and Computation 4, 219–237 (2008)zbMATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Dave A. D. Tompkins
    • 1
  • Holger H. Hoos
    • 1
  1. 1.Department of Computer ScienceUniversity of British ColumbiaCanada

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