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Generating Diverse Solutions in SAT

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Theory and Applications of Satisfiability Testing - SAT 2011 (SAT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6695))

Abstract

This paper considers the Diverse k Set problem in SAT, that is, the problem of efficiently generating a number of diverse solutions (satisfying assignments) given a propositional formula. We provide an extensive analysis of existing algorithms for this problem in a newly developed framework and propose new algorithms. While existing algorithms adapt modern SAT solvers to solve Diverse k Set by changing their polarity selection heuristic, our new algorithms adapt the variable ordering strategy as well. Our experimental results demonstrate that the proposed algorithms improve the diversification quality of the solutions on large industrial instances of Diverse k Set arising in SAT-based semiformal verification of hardware.

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References

  1. Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press, Amsterdam (2009)

    MATH  Google Scholar 

  2. Agbaria, S., Carmi, D., Cohen, O., Korchemny, D., Lifshits, M., Nadel, A.: SAT-based semiformal verification of hardware. In: Bloem, R., Sharygina, N. (eds.) Proceedings of the 10th International Conference on Formal Methods in Computer-Aided Design (FMCAD 2010), pp. 25–32 (October 2010)

    Google Scholar 

  3. Hebrard, E., Hnich, B., O’Sullivan, B., Walsh, T.: Finding diverse and similar solutions in constraint programming. In: Veloso, M.M., Kambhampati, S. (eds.) AAAI, pp. 372–377. AAAI Press / The MIT Press (2005)

    Google Scholar 

  4. Schreiber, Y.: Value-ordering heuristics: Search performance vs. Solution diversity. In: Cohen, D. (ed.) CP 2010. LNCS, vol. 6308, pp. 429–444. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  5. Dechter, R., Kask, K., Bin, E., Emek, R.: Generating random solutions for constraint satisfaction problems. In: AAAI/IAAI, pp. 15–21 (2002)

    Google Scholar 

  6. Kitchen, N., Kuehlmann, A.: Stimulus generation for constrained random simulation. In: ICCAD, pp. 258–265 (2007)

    Google Scholar 

  7. Gomes, C.P., Sabharwal, A., Selman, B.: Near-uniform sampling of combinatorial spaces using XOR constraints. In: Schölkopf, B., Platt, J.C., Hoffman, T. (eds.) NIPS, pp. 481–488 (2006)

    Google Scholar 

  8. Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: DAC, pp. 530–535. ACM, New York (2001)

    Google Scholar 

  9. Silva, J.P.M., Sakallah, K.A.: GRASP: A search algorithm for propositional satisfiability. IEEE Transactions on Computers 48, 506–521 (1999)

    Article  Google Scholar 

  10. Huang, J.: The effect of restarts on the efficiency of clause learning. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence, pp. 2318–2323 (2007)

    Google Scholar 

  11. Dershowitz, N., Hanna, Z., Nadel, A.: A clause-based heuristic for SAT solvers. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 46–60. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. Frost, D., Dechter, R.: In search of the best constraint satisfaction search. In: AAAI, pp. 301–306 (1994)

    Google Scholar 

  13. Strichman, O.: Tuning SAT checkers for bounded model checking. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 480–494. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  14. Pipatsrisawat, K., Darwiche, A.: A lightweight component caching scheme for satisfiability solvers. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 294–299. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  15. Nadel, A.: Generating diverse solutions in SAT: Paper addendum (2011), http://www.cs.tau.ac.il/research/alexander.nadel/multiple_cex_addendum.pdf

  16. Heule, M., van Maaren, H.: Look-ahead based SAT solvers [1], pp. 155–184

    Google Scholar 

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Nadel, A. (2011). Generating Diverse Solutions in SAT. In: Sakallah, K.A., Simon, L. (eds) Theory and Applications of Satisfiability Testing - SAT 2011. SAT 2011. Lecture Notes in Computer Science, vol 6695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21581-0_23

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  • DOI: https://doi.org/10.1007/978-3-642-21581-0_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21580-3

  • Online ISBN: 978-3-642-21581-0

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