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Fast Sampling of Perfectly Uniform Satisfying Assignments

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Theory and Applications of Satisfiability Testing – SAT 2018 (SAT 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10929))

Abstract

We present an algorithm for perfectly uniform sampling of satisfying assignments, based on the exact model counter sharpSAT and reservoir sampling. In experiments across several hundred formulas, our sampler is faster than the state of the art by 10 to over 100,000 times.

Research supported by NSF grants CCF-1514128, CCF-1733884, an Adobe research grant, and the Greek State Scholarships Foundation (IKY).

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Notes

  1. 1.

    The arithmetic mean [of the speedup] is even greater (always). For the aptness of using the geometric mean to report speedup factors see [5].

References

  1. Bayardo Jr., R.J., Pehoushek, J.D.: Counting models using connected components. In: Proceedings of the 17th National Conference on Artificial Intelligence and 12th Conference on Innovative Applications of Artificial Intelligence, pp. 157–162. AAAI Press (2000)

    Google Scholar 

  2. Chakraborty, S., Fremont, D.J., Meel, K.S., Seshia, S.A., Vardi, M.Y.: On parallel scalable uniform SAT witness generation. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 304–319. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46681-0_25

    Chapter  Google Scholar 

  3. Chakraborty, S., Meel, K.S., Vardi, M.Y.: Balancing scalability and uniformity in SAT witness generator. In: Proceedings of the 51st Annual Design Automation Conference, DAC 2014, pp. 60:1–60:6. ACM, New York (2014). http://doi.acm.org/10.1145/2593069.2593097

  4. Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Commun. ACM 5(7), 394–397 (1962)

    Article  MathSciNet  Google Scholar 

  5. Fleming, P.J., Wallace, J.J.: How not to lie with statistics: the correct way to summarize benchmark results. Commun. ACM 29(3), 218–221 (1986). http://doi.acm.org.oca.ucsc.edu/10.1145/5666.5673

    Article  Google Scholar 

  6. SPUR source code. https://github.com/ZaydH/spur

  7. Meel, K.: Index of UniGen verification benchmarks. https://www.cs.rice.edu/CS/Verification/Projects/UniGen/Benchmarks/

  8. Naveh, Y., Rimon, M., Jaeger, I., Katz, Y., Vinov, M., Marcus, E., Shurek, G.: Constraint-based random stimuli generation for hardware verification. In: Proceedings of the 18th Conference on Innovative Applications of Artificial Intelligence, IAAI 2006, vol. 2, pp. 1720–1727. AAAI Press (2006)

    Google Scholar 

  9. Sang, T., Bacchus, F., Beame, P., Kautz, H., Pitassi, T.: Combining component caching and clause learning for effective model counting. In: Proceedings of the 7th International Conference on Theory and Applications of Satisfiability Testing, SAT 2004 (2004)

    Google Scholar 

  10. Sang, T., Beame, P., Kautz, H.: Heuristics for fast exact model counting. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 226–240. Springer, Heidelberg (2005). https://doi.org/10.1007/11499107_17

    Chapter  Google Scholar 

  11. Thurley, M.: sharpSAT – counting models with advanced component caching and implicit BCP. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 424–429. Springer, Heidelberg (2006). https://doi.org/10.1007/11814948_38

    Chapter  Google Scholar 

  12. Vitter, J.S.: Random sampling with a reservoir. ACM Trans. Math. Softw. 11(1), 37–57 (1985). http://doi.acm.org/10.1145/3147.3165

    Article  MathSciNet  Google Scholar 

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Correspondence to Zayd S. Hammoudeh .

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Achlioptas, D., Hammoudeh, Z.S., Theodoropoulos, P. (2018). Fast Sampling of Perfectly Uniform Satisfying Assignments. In: Beyersdorff, O., Wintersteiger, C. (eds) Theory and Applications of Satisfiability Testing – SAT 2018. SAT 2018. Lecture Notes in Computer Science(), vol 10929. Springer, Cham. https://doi.org/10.1007/978-3-319-94144-8_9

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  • DOI: https://doi.org/10.1007/978-3-319-94144-8_9

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