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SAT-Based Synthesis Methods for Safety Specs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8318))

Abstract

Automatic synthesis of hardware components from declarative specifications is an ambitious endeavor in computer aided design. Existing synthesis algorithms are often implemented with Binary Decision Diagrams (BDDs), inheriting their scalability limitations. Instead of BDDs, we propose several new methods to synthesize finite-state systems from safety specifications using decision procedures for the satisfiability of quantified and unquantified Boolean formulas (SAT-, QBF- and EPR-solvers). The presented approaches are based on computational learning, templates, or reduction to first-order logic. We also present an efficient parallelization, and optimizations to utilize reachability information and incremental solving. Finally, we compare all methods in an extensive case study. Our new methods outperform BDDs and other existing work on some classes of benchmarks, and our parallelization achieves a super-linear speedup.

This work was supported in part by the Austrian Science Fund (FWF) through projects RiSE (S11406-N23 and S11408-N23) and QUAINT (I774-N23), and by the European Commission through project STANCE (317753).

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References

  1. Becker, B., Ehlers, R., Lewis, M., Marin, P.: ALLQBF solving by computational learning. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 370–384. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  2. Biere, A., Cimatti, A., Clarke, E., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  3. Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. FAIA, vol. 185. IOS Press (2009)

    Google Scholar 

  4. Bloem, R., Galler, S.J., Jobstmann, B., Piterman, N., Pnueli, A., Weiglhofer, M.: Specify, compile, run: Hardware from PSL. Electronic Notes in Theoretical Computer Science 190(4), 3–16 (2007)

    Article  Google Scholar 

  5. Bloem, R., Könighofer, R., Seidl, M.: SAT-based synthesis methods for safety specs. CoRR, abs/1311.3530 (2013), http://arxiv.org/abs/1311.3530

  6. Bradley, A.R.: SAT-based model checking without unrolling. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 70–87. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  7. Brayton, R., Mishchenko, A.: ABC: An academic industrial-strength verification tool. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 24–40. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  8. Ehlers, R.: Symbolic bounded synthesis. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 365–379. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  9. Ehlers, R., Könighofer, R., Hofferek, G.: Symbolically synthesizing small circuits. In: FMCAD 2012, pp. 91–100. IEEE (2012)

    Google Scholar 

  10. Ernst, M.D., Perkins, J.H., Guo, P.J., McCamant, S., Pacheco, C., Tschantz, M.S., Xiao, C.: The Daikon system for dynamic detection of likely invariants. Sci. Comput. Program. 69(1-3), 35–45 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Filiot, E., Jin, N., Raskin, J.-F.: An antichain algorithm for LTL realizability. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 263–277. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  12. Fröhlich, A., Kovasznai, G., Biere, A.: A DPLL algorithm for solving DQBF. In: Pragmatics of SAT (PoS 2012, aff. to SAT 2012) (2012)

    Google Scholar 

  13. Janota, M., Marques-Silva, J.: Abstraction-based algorithm for 2QBF. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 230–244. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  14. Jiang, J.-H.R., Lin, H.-P., Hung, W.-L.: Interpolating functions from large boolean relations. In: International Conference on Computer-Aided Design (ICCAD 2009), pp. 779–784. IEEE (2009)

    Google Scholar 

  15. Kojevnikov, A., Kulikov, A.S., Yaroslavtsev, G.: Finding efficient circuits using SAT-solvers. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 32–44. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  16. Könighofer, R., Bloem, R.: Automated error localization and correction for imperative programs. In: FMCAD 2011, pp. 91–100. IEEE (2011)

    Google Scholar 

  17. Korovin, K.: iProver – an instantiation-based theorem prover for first-order logic (System description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 292–298. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  18. Lewis, H.R.: Complexity results for classes of quantificational formulas. J. Comput. Syst. Sci. 21(3), 317–353 (1980)

    Article  MATH  Google Scholar 

  19. Lonsing, F., Biere, A.: DepQBF: A dependency-aware QBF solver. JSAT 7(2-3), 71–76 (2010)

    Google Scholar 

  20. Moon, I., Kukula, J.H., Shiple, T.R., Somenzi, F.: Least fixpoint approximations for reachability analysis. In: ICCAD 1999, pp. 41–44. IEEE (1999)

    Google Scholar 

  21. Morgenstern, A., Gesell, M., Schneider, K.: Solving games using incremental induction. In: Johnsen, E.B., Petre, L. (eds.) IFM 2013. LNCS, vol. 7940, pp. 177–191. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  22. Niemetz, A., Preiner, M., Lonsing, F., Seidl, M., Biere, A.: Resolution-based certificate extraction for QBF (tool presentation). In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 430–435. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  23. Plaisted, D.A., Greenbaum, S.: A structure-preserving clause form translation. J. Symb. Comput. 2(3), 293–304 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  24. Reiter, R.: A theory of diagnosis from first principles. Artif. Intell. 32(1), 57–95 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  25. Seidl, M., Könighofer, R.: Partial witnesses from preprocessed quantified Boolean formulas. In: DATE 2014 (to appear, 2014)

    Google Scholar 

  26. Seidl, M., Lonsing, F., Biere, A.: qbf2epr: A tool for generating EPR formulas from QBF. In: Workshop on Practical Aspects of Automated Reasoning (2012)

    Google Scholar 

  27. Sohail, S., Somenzi, F.: Safety first: A two-stage algorithm for LTL games. In: FMCAD 2009, pp. 77–84. IEEE (2009)

    Google Scholar 

  28. Solar-Lezama, A.: The sketching approach to program synthesis. In: Hu, Z. (ed.) APLAS 2009. LNCS, vol. 5904, pp. 4–13. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  29. Staber, S., Bloem, R.: Fault localization and correction with QBF. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 355–368. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  30. Thomas, W.: On the synthesis of strategies in infinite games. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 1–13. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

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Bloem, R., Könighofer, R., Seidl, M. (2014). SAT-Based Synthesis Methods for Safety Specs. In: McMillan, K.L., Rival, X. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2014. Lecture Notes in Computer Science, vol 8318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54013-4_1

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  • DOI: https://doi.org/10.1007/978-3-642-54013-4_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54012-7

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