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Automated Testing and Debugging of SAT and QBF Solvers

  • Robert Brummayer
  • Florian Lonsing
  • Armin Biere
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6175)

Abstract

Robustness and correctness are essential criteria for SAT and QBF solvers. We develop automated testing and debugging techniques designed and optimized for SAT and QBF solver development. Our fuzz testing techniques are able to find critical solver defects that lead to crashes, invalid satisfying assignments and incorrect satisfiability results. Moreover, we show that sequential and concurrent delta debugging techniques are highly effective in minimizing failure-inducing inputs.

Keywords

Directed Acyclic Graph Automate Test Critical Defect Boolean Circuit 3SAT Generator 
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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References

  1. 1.
    Ansótegui, C., Béjar, R., Fernández, C., Mateu, C.: Generating Hard SAT/CSP Instances Using Expander Graphs. In: AAAI (2008)Google Scholar
  2. 2.
    Babić, D.: Exploiting Structure for Scalable Software Verification. PhD thesis, University of British Columbia, Vancouver, Canada (2008)Google Scholar
  3. 3.
    Benedetti, M.: sKizzo: A Suite to Evaluate and Certify QBFs. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 369–376. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Le Berre, D.: SAT4J: Bringing the Power of SAT Technology to the Java Platform, http://www.sat4j.org
  5. 5.
    Le Berre, D., Roussel, O., Simon, L.: SAT 2009 Competitive Events Booklet - Preliminary Version. In: SAT competition solver descriptions (September 2009), http://www.cril.univ-artois.fr/SAT09/solvers/booklet.pdf
  6. 6.
    Biere, A.: Resolve and Expand. In: SAT (Selected Papers) (2004)Google Scholar
  7. 7.
    Biere, A.: PicoSAT Essentials. JSAT 4 (2008)Google Scholar
  8. 8.
    Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. IOS Press, Amsterdam (2009)zbMATHGoogle Scholar
  9. 9.
    Bofill, M., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E., Rubio, A.: The Barcelogic SMT Solver. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 294–298. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Bregman, D., Mitchell, D.: The SAT solver MXC, Version 0.5., SAT competition solver description (2007)Google Scholar
  11. 11.
    Brummayer, R., Biere, A.: Fuzzing and Delta-Debugging SMT Solvers. In: SMT. ACM International Conference Proceedings Series. ACM, New York (2009)Google Scholar
  12. 12.
    Kleine Büning, H., Karpinski, M., Flögel, A.: Resolution for Quantified Boolean Formulas. Inf. Comput. 117(1), 12–18 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Cadoli, M., Schaerf, M., Giovanardi, A., Giovanardi, M.: An Algorithm to Evaluate Quantified Boolean Formulae and Its Experimental Evaluation. J. Autom. Reasoning 28 (2002)Google Scholar
  14. 14.
    Chen, H., Interian, Y.: A Model for Generating Random Quantified Boolean Formulas. In: IJCAI (2005)Google Scholar
  15. 15.
    Claessen, K., Hughes, J.: QuickCheck: a Lightweight Tool for Random Testing of Haskell Programs. ICFP 35(9) (2000)Google Scholar
  16. 16.
    Creignou, N., Daudé, H., Egly, U., Rossignol, R.: New Results on the Phase Transition for Random Quantified Boolean Formulas. In: Kleine Büning, H., Zhao, X. (eds.) SAT 2008. LNCS, vol. 4996, pp. 34–47. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. 17.
    Davis, M., Logemann, G., Loveland, D.: A Machine Program for Theorem-Proving. ACM Commun. 5 (1962)Google Scholar
  18. 18.
    Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  19. 19.
    Freeman, J.W.: Improvements to Propositional Satisfiability Search Algorithms. PhD thesis, Depart. of Comp. and Inf. Science, University of Pennsylvania (1995)Google Scholar
  20. 20.
    Gebser, M., Kaufmann, B., Schaub, T.: The Conflict-Driven Answer Set Solver clasp: Progress Report. In: Erdem, E., Lin, F., Schaub, T. (eds.) LPNMR 2009. LNCS, vol. 5753, pp. 509–514. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  21. 21.
    Van Gelder, A.: Extracting (Easily) Checkable Proofs from a Satisfiability Solver that Employs both Preorder and Postorder Resolution. In: AMAI (2002)Google Scholar
  22. 22.
    Gent, I., Walsh, T.: The SAT Phase Transition. In: ECAI (1994)Google Scholar
  23. 23.
    Gent, I., Walsh, T.: Beyond NP: the QSAT phase transition. In: AAAI/IAAI (1999)Google Scholar
  24. 24.
    Giunchiglia, E., Narizzano, M., Tacchella, A.: QuBE++: An Efficient QBF Solver. In: Hu, A.J., Martin, A.K. (eds.) FMCAD 2004. LNCS, vol. 3312, pp. 201–213. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  25. 25.
    Hamadi, Y., Jabbour, S.: ManySAT: a Parallel SAT Solver. JSAT 6 (2009)Google Scholar
  26. 26.
    Heule, M.: SmArT Solving: Tools and Techniques for Satisfiability Solvers. PhD thesis, TU Delft (2008)Google Scholar
  27. 27.
    Horie, S., Watanabe, O.: Hard instance generation for SAT. CoRR, cs.CC/9809117 (1998)Google Scholar
  28. 28.
    Hsu, E., McIlraith, S.: VARSAT: Integrating Novel Probabilistic Interference Techniques with DPLL Search. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 377–390. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  29. 29.
    Huang, J.: TINISAT in SAT Competition 2007. SAT competition solver description (2007)Google Scholar
  30. 30.
    Jain, H., Clarke, E.: SAT Solver Descriptions: CMUSAT-Base and CMUSAT. SAT competition solver description (2007)Google Scholar
  31. 31.
    Jussila, T., Biere, A., Sinz, C., Kröning, D., Wintersteiger, C.: A First Step Towards a Unified Proof Checker for QBF. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 201–214. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  32. 32.
    Kern, C., Khaleghi, M., Kugele, S., Schallhart, C., Tautschnig, M., Weis, A.: SAT 7 - Engineering a Modular SAT-Solver. SAT competition solver description (2007)Google Scholar
  33. 33.
    Letz, R.: Lemma and Model Caching in Decision Procedures for Quantified Boolean Formulas. In: Egly, U., Fermüller, C. (eds.) TABLEAUX 2002. LNCS (LNAI), vol. 2381, p. 160. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  34. 34.
    Lewis, M., Schubert, T., Becker, B.: Multithreaded SAT Solving. In: Asia and South Pacific DAC (2007)Google Scholar
  35. 35.
    Lonsing, F.: DepQBF 0.1 Source Code (2010), http://fmv.jku.at/depqbf/
  36. 36.
    Miller, B., Koski, D., Lee, C., Maganty, V., Murthy, R., Natarajan, A., Steidl, J.: Fuzz Revisited: A Re-examination of the Reliability of UNIX Utilities and Services. Technical Report CS-TR-1995-1268, University of Wisconsin, Madison (1995)Google Scholar
  37. 37.
    Misherghi, G., Su, Z.: HDD: Hierarchical Delta Debugging. In: ICSE, pp. 142–151. ACM, New York (2006)CrossRefGoogle Scholar
  38. 38.
    Narizzano, M., Peschiera, C., Pulina, L., Tacchella, A.: Evaluating and Certifying QBFs: A Comparison of State-of-the-Art Tools. AI Commun. 22 (2009)Google Scholar
  39. 39.
    Pan, G., Vardi, M.: Symbolic Decision Procedures for QBF. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 453–467. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  40. 40.
    Pennock, D., Stout, Q.: Exploiting a Theory of Phase Transitions in Three-Satisfiability Problems. In: AAAI/IAAI, vol. 1 (1996)Google Scholar
  41. 41.
    Pipatsrisawat, K., Darwiche, A.: RSat 2.0: SAT Solver Description. Technical Report D–153, Automated Reasoning Group, CSD, UCLA (2007)Google Scholar
  42. 42.
    Ranise, S., Tinelli, C.: The SMT-LIB Standard: Version 1.2. Technical report, Department of Computer Science, The University of Iowa (2006)Google Scholar
  43. 43.
    Samulowitz, H.: MiniQBF Solver (2010), http://miniqbf.spaces.live.com/
  44. 44.
    Samulowitz, H., Bacchus, F.: Using SAT in QBF. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 578–592. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  45. 45.
    Sutton, M., Greene, A., Amini, P.: Fuzzing - Brute Force Vulnerability Discovery. Pearson Ed., London (2007)Google Scholar
  46. 46.
    Takanen, A., Demott, J., Miller, C.: Fuzzing for Software Security Testing and Quality Assurance. Artech House (2008)Google Scholar
  47. 47.
    Tseitin, G.: On the Complexity of Proofs in Propositional Logics. Automation of Reasoning: Classical Papers in Computational Logic 1967-1970 2 (1983)Google Scholar
  48. 48.
    Xu, K., Boussemart, F., Hemery, F., Lecoutre, C.: A Simple Model to Generate Hard Satisfiable Instances. CoRR, abs/cs/0509032 (2005)Google Scholar
  49. 49.
    Yu, Y., Malik, S.: Validating the Result of a Quantified Boolean Formula (QBF) Solver: Theory and Practice. In: Asia and South Pacific DAC (2005)Google Scholar
  50. 50.
    Zeller, A.: Why Programs Fail. A Guide to Systematic Debugging. Morgan Kaufmann, San Francisco (2005)Google Scholar
  51. 51.
    Zeller, A., Hildebrandt, R.: Simplifying and Isolating Failure-Inducing Input. IEEE Transactions on Software Engineering 28(2), 183–200 (2002)CrossRefGoogle Scholar
  52. 52.
    Zhang, L., Malik, S.: Validating SAT Solvers Using an Independent Resolution-Based Checker: Practical Implementations and Other Applications. In: DATE 2003 (2003)Google Scholar
  53. 53.
    Zhang, L., Malik, S.: Towards Symmetric Treatment of Conflicts And Satisfaction in Quantified Boolean Satisfiability Solver. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, p. 200. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Robert Brummayer
    • 1
  • Florian Lonsing
    • 1
  • Armin Biere
    • 1
  1. 1.Institute for Formal Models and VerificationJohannes Kepler UniversityLinzAustria

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