Labelled Clauses

  • Tal Lev-Ami
  • Christoph Weidenbach
  • Thomas Reps
  • Mooly Sagiv
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4603)

Abstract

We add labels to first-order clauses to simultaneously apply superpositions to several proof obligations inside one clause set. From a theoretical perspective, the approach unifies a variety of deduction modes. These include different strategies such as set of support, as well as explicit case analysis, e.g., splitting. From a practical perspective, labelled clauses offer advantages in the case of related proof obligations resulting from multiple conjectures over the same axiom set or from a single conjecture that is a large conjunction. Here we can share clauses (e.g., the axioms and clauses deduced from them, share Skolem symbols), share deduced clause variants, and transfer lemmas between the different obligations. Motivated by software verification, we have created a prototype implementation of labelled clauses that supports multiple conjectures, and we provide convincing experiments for the benefits.

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References

  1. 1.
    Ball, T., Podelski, A., Rajamani, S.K.: Boolean and cartesian abstraction for model checking C programs. In: Margaria, T., Yi, W. (eds.) ETAPS 2001 and TACAS 2001. LNCS, vol. 2031, pp. 268–283. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    Basin, D., D’Agostino, M., Gabbay, D.M., Matthews, S., Viganò, L.: Labelled Deduction. Applied Logic Series, vol. 17. Kluwer, Dordrecht (2000)MATHGoogle Scholar
  3. 3.
    Bonacina, M.P.: Towards a unified model of search in theorem-proving: subgoal-reduction strategies. J. Symb. Comput. 39(2), 209–255 (2005)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction of approximation of fixed points. In: POPL, pp. 238–252 (1977)Google Scholar
  5. 5.
    Graf, S., Saïdi, H.: Construction of abstract state graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)Google Scholar
  6. 6.
    Green, C.: Theorem-proving by resolution as a basis for question-answering systems. Machine Intelligence 4, 183–205 (1969)MATHGoogle Scholar
  7. 7.
    Hähnle, R.: Tableaux and related methods. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, ch. 6, vol. 1, pp. 103–177. Elsevier, North-Holland (2001)Google Scholar
  8. 8.
    Lahiri, S., Ball, T., Cook, B.: Predicate abstraction via symbolic decision procedures. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 24–38. Springer, Heidelberg (2005)Google Scholar
  9. 9.
    Lev-Ami, T., Immerman, N., Reps, T.W., Sagiv, M., Srivastava, S., Yorsh, G.: Simulating reachability using first-order logic with applications to verification of linked data structures. In: Nieuwenhuis, R. (ed.) Automated Deduction – CADE-20. LNCS (LNAI), vol. 3632, pp. 99–115. Springer, Heidelberg (2005)Google Scholar
  10. 10.
    Lev-Ami, T., Sagiv, M.: TVLA: A system for implementing static analyses. In: Palsberg, J. (ed.) SAS 2000. LNCS, vol. 1824, Springer, Heidelberg (2000)Google Scholar
  11. 11.
    Lev-Ami, T., Weidenbach, C., Reps, T., Sagiv, M.: Experimental version of SPASS for multiple conjectures (2007), Available at http://www.cs.tau.ac.il/~tla/SPASS
  12. 12.
    Loginov, A., Reps, T., Sagiv, M.: Abstraction refinement via inductive learning. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 519–533. Springer, Heidelberg (2005)Google Scholar
  13. 13.
    Nelson, C.G., Oppen, D.C.: A simplifier based on efficient decision algorithms. In: POPL, pp. 141–150 (1978)Google Scholar
  14. 14.
    Nieuwenhuis, R., Oliveras, A.: Decision procedures for SAT, SAT modulo theories and beyond. The BarcelogicTools. In: Sutcliffe, G., Voronkov, A. (eds.) LPAR 2005. LNCS (LNAI), vol. 3835, pp. 23–46. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Riazanov, A., Voronkov, A.: Splitting without backtracking. In: IJCAI, pp. 611–617 (2001)Google Scholar
  16. 16.
    Riazanov, A., Voronkov, A.: The design and implementation of VAMPIRE. AI Communications 15(2-3), 91–110 (2002)MATHGoogle Scholar
  17. 17.
    Sagiv, M., Reps, T., Wilhelm, R.: Parametric shape analysis via 3-valued logic. TOPLAS, 217–298 (2002)Google Scholar
  18. 18.
    Schulz, S.: E – A Brainiac Theorem Prover. Journal of AI Communications 15(2/3), 111–126 (2002)MATHGoogle Scholar
  19. 19.
    Voronkov, A.: Personal communication (2007)Google Scholar
  20. 20.
    Weidenbach, C.: Combining superposition, sorts and splitting. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, ch. 27, vol. 2, pp. 1965–2012. Elsevier, North-Holland (2001)CrossRefGoogle Scholar
  21. 21.
    Weidenbach, C., Brahm, U., Hillenbrand, T., Keen, E., Theobald, C., Topic, D.: SPASS version 2.0. In: Voronkov, A. (ed.) Automated Deduction - CADE-18. LNCS (LNAI), vol. 2392, pp. 275–279. Springer, Heidelberg (2002)Google Scholar
  22. 22.
    Whittemore, J., Kim, J., Sakallah, K.A.: SATIRE: A new incremental satisfiability engine. In: DAC, pp. 542–545 (2001)Google Scholar
  23. 23.
    Wolf, A.: Strategy selection for automated theorem proving. In: Giunchiglia, F. (ed.) AIMSA 1998. LNCS (LNAI), vol. 1480, pp. 452–465. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  24. 24.
    Wos, L., Robinson, G.A., Carson, D.F.: Efficiency and completeness of the set of support strategy in theorem proving. J. ACM 12(4), 536–541 (1965)MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Yorsh, G., Reps, T., Sagiv, M.: Symbolically computing most-precise abstract operations for shape analysis. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 530–545. Springer, Heidelberg (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Tal Lev-Ami
    • 1
  • Christoph Weidenbach
    • 2
  • Thomas Reps
    • 3
  • Mooly Sagiv
    • 1
  1. 1.School of Comp. Sci., Tel Aviv University 
  2. 2.Max-Planck-Institut für Informatik, Saarbrücken 
  3. 3.Comp. Sci. Dept., University of Wisconsin, Madison 

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