CTL Model Checking in Deduction Modulo

  • Kailiang Ji
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9195)


In this paper we give an overview of proof-search method for CTL model checking based on Deduction Modulo. Deduction Modulo is a reformulation of Predicate Logic where some axioms—possibly all—are replaced by rewrite rules. The focus of this paper is to give an encoding of temporal properties expressed in CTL, by translating the logical equivalence between temporal operators into rewrite rules. This way, the proof-search algorithms designed for Deduction Modulo, such as Resolution Modulo or Tableaux Modulo, can be used in verifying temporal properties of finite transition systems. An experimental evaluation using Resolution Modulo is presented.


Model checking Deduction modulo Resolution modulo 



I am grateful to Gilles Dowek, for his careful reading and comments.


  1. 1.
    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) CrossRefGoogle Scholar
  2. 2.
    Burel, G.: Embedding deduction modulo into a prover. In: Dawar, A., Veith, H. (eds.) CSL 2010. LNCS, vol. 6247, pp. 155–169. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  3. 3.
    Burel, G.: Experimenting with deduction modulo. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 162–176. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  4. 4.
    Clarke Jr, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge, MA, USA (1999) Google Scholar
  5. 5.
    Delahaye, D., Doligez, D., Gilbert, F., Halmagrand, P., Hermant, O.: Zenon modulo: when Achilles outruns the tortoise using deduction modulo. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR-19 2013. LNCS, vol. 8312, pp. 274–290. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  6. 6.
    Dowek, G.: Polarized resolution modulo. In: Calude, C.S., Sassone, V. (eds.) TCS 2010. IFIP AICT, vol. 323, pp. 182–196. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  7. 7.
    Dowek, G., Hardin, T., Kirchner, C.: Theorem proving modulo. J. Autom. reasoning 31, 33–72 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Dowek, G., Jiang, Y.: A Logical Approach to CTL (2013). (manuscript)
  9. 9.
    Dowek, G., Jiang, Y.: Axiomatizing Truth in a Finite Model (2013). (manuscript)
  10. 10.
    Ji, K.: CTL Model Checking in Deduction Modulo. In: Felty, A.P., Middeldorp, A. (eds.) CADE-25, 2015. LNCS, vol. 9195, pp. xx–yy (2015). (fullpaper)
  11. 11.
    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) CrossRefGoogle Scholar
  12. 12.
    Rajan, S., Shankar, N., Srivas, M.: An Integration of Model Checking with Automated Proof Checking. In: Wolper, P. (ed.) CAV 1995. LNCS, vol. 939, pp. 84–97. Springer, Berlin Heidelberg (1995)Google Scholar
  13. 13.
    Troelstra, A.S., Schwichtenberg, H.: Basic Proof Theory. Cambridge University Press, New York (1996)zbMATHGoogle Scholar
  14. 14.
    Zhang, W.: Bounded semantics of CTL and SAT-based verification. In: Breitman, K., Cavalcanti, A. (eds.) ICFEM 2009. LNCS, vol. 5885, pp. 286–305. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  15. 15.
    Zhang, W.: VERDS Modeling Language (2012).
  16. 16.
    Zhang, W.: QBF encoding of temporal properties and QBF-based verification. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS, vol. 8562, pp. 224–239. Springer, Heidelberg (2014) Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.INRIA and Paris DiderotParis Cedex 13France

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