Evaluating LTL Satisfiability Solvers

  • Viktor Schuppan
  • Luthfi Darmawan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6996)

Abstract

We perform a comprehensive experimental evaluation of off-the-shelf solvers for satisfiability of propositional LTL. We consider a wide range of solvers implementing three major classes of algorithms: reduction to model checking, tableau-based approaches, and temporal resolution. Our set of benchmark families is significantly more comprehensive than those in previous studies. It takes the benchmark families of previous studies, which only have a limited overlap, and adds benchmark families not used for that purpose before.

We find that no solver dominates or solves all instances. Solvers focused on finding models and solvers using temporal resolution or fixed point computation show complementary strengths and weaknesses. This motivates and guides estimation of the potential of a portfolio solver. It turns out that even combining two solvers in a simple fashion significantly increases the share of solved instances while reducing CPU time spent.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
  2. 2.
  3. 3.
  4. 4.
  5. 5.
  6. 6.
  7. 7.
  8. 8.
  9. 9.
  10. 10.
  11. 11.
  12. 12.
  13. 13.
  14. 14.
  15. 15.
    Abate, P., Goré, R.: The Tableau Workbench. In: M4M (2007) Google Scholar
  16. 16.
    Beer, I., et al.: Efficient Detection of Vacuity in Temporal Model Checking. FMSD 18(2) (2001)Google Scholar
  17. 17.
    Behdenna, A., Dixon, C., Fisher, M.: Deductive Verification of Simple Foraging Robotic Behaviours. Int. J. of Intelligent Comput. and Cybernetics 2(4) (2009)Google Scholar
  18. 18.
    Le Berre, D., Simon, L.: The Essentials of the SAT 2003 Competition. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 452–467. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  19. 19.
    Le Berre, D., et al.: The SAT 2009 competition results: does theory meet practice (presentation). In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584. Springer, Heidelberg (2009)Google Scholar
  20. 20.
    Biere, A., Claessen, K.: Hardware Model Checking Competition (presentation). In: Hardware Verification Workshop 2010, Edinburgh, UK (2010)Google Scholar
  21. 21.
    Biere, A., Jussila, T.: Benchmark Tool Run, http://fmv.jku.at/run/
  22. 22.
    Biere, A., et al.: Handbook of Satisfiability. IOS Press, Amsterdam (2009)MATHGoogle Scholar
  23. 23.
    Bloem, R., et al.: Automatic hardware synthesis from specifications: a case study. In: DATE (2007)Google Scholar
  24. 24.
    Bloem, R., et al.: Specify, Compile, Run: Hardware from PSL. In: COCV. ENTCS, vol. 190(4). Elsevier, Amsterdam (2007)Google Scholar
  25. 25.
    Cimatti, A., et al.: Boolean Abstraction for Temporal Logic Satisfiability. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 532–546. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  26. 26.
    Cimatti, A., et al.: NuSMV 2: An OpenSource Tool for Symbolic Model Checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 359–364. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  27. 27.
    Clarke, E., Grumberg, O., Hamaguchi, K.: Another Look at LTL Model Checking. FMSD 10(1) (1997)Google Scholar
  28. 28.
    Daniele, M., Giunchiglia, F., Vardi, M.: Improved Automata Generation for Linear Temporal Logic. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 249–260. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  29. 29.
    Emerson, E.: Temporal and Modal Logic. In: Handbook of Theoretical Computer Science, vol. B: Formal Models and Sematics (B) (1990) Google Scholar
  30. 30.
    Emerson, E., Lei, C.: Efficient Model Checking in Fragments of the Propositional Mu-Calculus (Extended Abstract). In: LICS (1986)Google Scholar
  31. 31.
    Filiot, E., Jin, N., Raskin, J.: An Antichain Algorithm for LTL Realizability. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 263–277. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  32. 32.
    Fisher, M., Dixon, C., Peim, M.: Clausal temporal resolution. ACM Trans. Comput. Log. 2(1) (2001) Google Scholar
  33. 33.
    Fisman, D., et al.: A Framework for Inherent Vacuity. In: Chockler, H., Hu, A.J. (eds.) HVC 2008. LNCS, vol. 5394, pp. 7–22. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  34. 34.
    Gomes, C., Selman, B.: Algorithm portfolios. Artif. Intell. 126(1-2) (2001)Google Scholar
  35. 35.
    Goranko, V., Kyrilov, A., Shkatov, D.: Tableau Tool for Testing Satisfiability in LTL: Implementation and Experimental Analysis. In: M4M (2009)Google Scholar
  36. 36.
    Goré, R.: Personal Communication (2010)Google Scholar
  37. 37.
    Goré, R., Widmann, F.: An Experimental Comparison of Theorem Provers for CTL. In: CLoDeM (2010)Google Scholar
  38. 38.
    Goré, R., Widmann, F.: An Optimal On-the-Fly Tableau-Based Decision Procedure for PDL-Satisfiability. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 437–452. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  39. 39.
    Heljanko, K., Junttila, T., Latvala, T.: Incremental and Complete Bounded Model Checking for Full PLTL. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 98–111. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  40. 40.
    Henzinger, T., Kupferman, O., Qadeer, S.: From Pre-Historic to Post-Modern Symbolic Model Checking. FMSD 23(3) (2003)Google Scholar
  41. 41.
    Heuerding, A., et al.: Propositional Logics on the Computer. In: Baumgartner, P., Posegga, J., Hähnle, R. (eds.) TABLEAUX 1995. LNCS, vol. 918, pp. 310–323. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  42. 42.
    Hirsch, B., Hustadt, U.: Translating PLTL into WS1S: Application Description. In: M4M (2001) Google Scholar
  43. 43.
    Huberman, B., Lukose, R., Hogg, T.: An Economics Approach to Hard Computational Problems. Science 275(5296) (1997)Google Scholar
  44. 44.
    Hustadt, U., Konev, B.: TRP++: A temporal resolution prover. In: Collegium Logicum, vol. 8. Kurt Gödel Society (2004)Google Scholar
  45. 45.
    Hustadt, U., Schmidt, R.A.: Formulae which Highlight Differences between Temporal Logic and Dynamic Logic Provers. Issues in the Design and Experimental Evaluation of Systems for Modal and Temporal Logics. Dipartimento, di Ingegneria dell’Informazione, Unversitá degli Studi di Siena (2001)Google Scholar
  46. 46.
    Hustadt, U., Schmidt, R.A.: Scientific Benchmarking with Temporal Logic Decision Procedures. In: KR. Morgan Kaufmann, San Francisco (2002)Google Scholar
  47. 47.
    Hustadt, U., et al.: TeMP: A Temporal Monodic Prover. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 326–330. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  48. 48.
    Janssen, G.: Logics for Digital Circuit Verification: Theory, Algorithms, and Applications. PhD thesis. Technische Universiteit Eindhoven (1999) Google Scholar
  49. 49.
    Leyton-Brown, K., et al.: A Portfolio Approach to Algorithm Selection. In: IJCAI. Morgan Kaufmann, San Francisco (2003)Google Scholar
  50. 50.
    Ludwig, M., Hustadt, U.: Fair Derivations in Monodic Temporal Reasoning. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 261–276. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  51. 51.
    Ludwig, M., Hustadt, U.: Implementing a fair monodic temporal logic prover. AI Commun. 23(2-3) (2010)Google Scholar
  52. 52.
    Ludwig, M., Hustadt, U.: Resolution-Based Model Construction for PLTL. In: TIME (2009) Google Scholar
  53. 53.
    de Moura, L.: SAL: Tutorial (2004) Google Scholar
  54. 54.
    de Moura, L., et al.: SAL 2. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 496–500. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  55. 55.
    Nikolić, M.: Statistical Methodology for Comparison of SAT Solvers. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 209–222. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  56. 56.
    Pill, I., et al.: Formal analysis of hardware requirements. In: DAC (2006) Google Scholar
  57. 57.
  58. 58.
    Pulina, L., Tacchella, A.: A self-adaptive multi-engine solver for quantified Boolean formulas. Constraints 14(1) (2009) Google Scholar
  59. 59.
    Rozier, K., Vardi, M.: A Multi-Encoding Approach for LTL Symbolic Satisfiability Checking. In: Butler, M., Schulte, W. (eds.) FM 2011. LNCS, vol. 6664, pp. 417–431. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  60. 60.
    Rozier, K., Vardi, M.: LTL Satisfiability Checking. STTT 12(2) (2010) Google Scholar
  61. 61.
    Schuppan, V.: Towards a notion of unsatisfiable and unrealizable cores for LTL. Sci. Comput. Program (2010) (in Press), doi:10.1016/j.scico.2010.11.004Google Scholar
  62. 62.
    Schuppan, V., Darmawan, L.: Evaluating LTL Satisfiability Solvers (full version) (2011), http://www.schuppan.de/viktor/VSchuppanLDarmawan-ATVA-2011-full.pdf
  63. 63.
    Schwendimann, S.: A New One-Pass Tableau Calculus for PLTL. In: de Swart, H. (ed.) TABLEAUX 1998. LNCS (LNAI), vol. 1397, pp. 277–292. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  64. 64.
    Simon, L., Le Berre, D.: Some Results and Lessons from the SAT Competitions (invited talk, slides only). In: Second International Workshop on Constraint Propagation and Implementation, Sitges, Spain (October 1, 2005)Google Scholar
  65. 65.
    StatSoft, Inc. Electronic Statistics Textbook. StatSoft, Tulsa, OK, USA, http://www.statsoft.com/textbook/
  66. 66.
    Sutcliffe, G., Suttner, C.: Evaluating general purpose automated theorem proving systems. Artif. Intell. 131(1-2) (2001) Google Scholar
  67. 67.
    The VIS Group: VIS: A System for Verification and Synthesis. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 428–432. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  68. 68.
    Wolper, P.: The Tableau Method for Temporal Logic: An Overview. Logique et Analyse 28(110-111) (1985) Google Scholar
  69. 69.
    De Wulf, M., et al.: Antichains: Alternative Algorithms for LTL Satisfiability and Model-Checking. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 63–77. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  70. 70.
    Xu, L., et al.: SATzilla: Portfolio-based Algorithm Selection for SAT. JAIR 32 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Viktor Schuppan
  • Luthfi Darmawan

There are no affiliations available

Personalised recommendations