Generate & Check Method for Verifying Transition Systems in CafeOBJ 

  • Kokichi Futatsugi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8950)


An interactive theorem proving method for the verification of infinite state transition systems is described.

The state space of a transition system is defined as a quotient set (i.e. a set of equivalence classes) of terms of a topmost sort State, and the transitions are defined with conditional rewrite rules over the quotient set. A property to be verified is either (1) an invariant (i.e. a state predicate that is valid for all reachable states) or (2) a (p leads-to q) property for two state predicates p and q, where (p leads-to q) means that from any reachable state s with (p(s) = true) the system will get into a state t with (q(t) = true) no matter what transition sequence is taken.

Verification is achieved by developing proof scores in CafeOBJ . Sufficient verification conditions are formalized for verifying invariants and (p leads-to q) properties. For each verification condition, a proof score is constructed to (1) generate a finite set of state patterns that covers all possible infinite states and (2) check validity of the verification condition for all the covering state patterns by reductions.

The method achieves significant automation of proof score developments.


Model Check Transition System Transition Rule Mutual Exclusion Transition Sequence 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bae, K., Escobar, S., Meseguer, J.: Abstract logical model checking of infinite-state systems using narrowing. In: van Raamsdonk, F. (ed.) RTA. LIPIcs, vol. 21, pp. 81–96. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2013)Google Scholar
  2. 2.
    Baier, C., Katoen, J.P.: Principles of model checking, pp. 1–975. MIT Press (2008)Google Scholar
  3. 3.
  4. 4.
    Chandy, K.M., Misra, J.: Parallel program design - a foundation. Addison-Wesley (1989)Google Scholar
  5. 5.
    Clarke, E.M., Grumberg, O., Peled, D.: Model checking. MIT Press (2001)Google Scholar
  6. 6.
  7. 7.
    Dong, J.S., Zhu, H. (eds.): ICFEM 2010. LNCS, vol. 6447. Springer, Heidelberg (2010)Google Scholar
  8. 8.
    Escobar, S., Meseguer, J.: Symbolic model checking of infinite-state systems using narrowing. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 153–168. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Futatsugi, K.: Verifying specifications with proof scores in CafeOBJ. In: Proc. of 21st IEEE/ACM International Conference on Automated Software Engineering (ASE 2006), pp. 3–10. IEEE Computer Society (2006)Google Scholar
  10. 10.
    Futatsugi, K.: Fostering proof scores in CafeOBJ. In: Dong, Zhu (eds.) [7], pp. 1–20Google Scholar
  11. 11.
    Futatsugi, K., Găină, D., Ogata, K.: Principles of proof scores in CafeOBJ. Theor. Comput. Sci. 464, 90–112 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Goguen, J.A., Meseguer, J.: Order-sorted algebra I: Equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theor. Comput. Sci. 105(2), 217–273 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Grumberg, O., Veith, H. (eds.): 25 Years of Model Checking. LNCS, vol. 5000. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  14. 14.
    Guttag, J.V., Horning, J.J., Garland, S.J., Jones, K.D., Modet, A., Wing, J.M.: Larch: Languages and Tools for Formal Specification. Springer (1993)Google Scholar
  15. 15.
  16. 16.
  17. 17.
    Meseguer, J.: Twenty years of rewriting logic. J. Log. Algebr. Program. 81(7-8), 721–781 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Nakamura, M., Ogata, K., Futatsugi, K.: Incremental proofs of termination, confluence and sufficient completeness of OBJ specifications. In: Iida, S., Meseguer, J., Ogata, K. (eds.) Specification, Algebra, and Software. LNCS, vol. 8373, pp. 92–109. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  19. 19.
    Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  20. 20.
    Ogata, K., Futatsugi, K.: Proof scores in the oTS/CafeOBJ method. In: Najm, E., Nestmann, U., Stevens, P. (eds.) FMOODS 2003. LNCS, vol. 2884, pp. 170–184. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  21. 21.
    Ogata, K., Futatsugi, K.: Simulation-based verification for invariant properties in the OTS/CafeOBJ method. Electr. Notes Theor. Comput. Sci. 201, 127–154 (2008)CrossRefGoogle Scholar
  22. 22.
    Ogata, K., Futatsugi, K.: A combination of forward and backward reachability analysis methods. In: Dong, Zhu (eds.) [7], pp. 501–517 (2010)Google Scholar
  23. 23.
  24. 24.
    Rocha, C., Meseguer, J.: Proving safety properties of rewrite theories. technical report. Tech. rep., University of Illinois at Urbana-Champaign (2010)Google Scholar
  25. 25.
    Rocha, C., Meseguer, J.: Proving safety properties of rewrite theories. In: Corradini, A., Klin, B., Cîrstea, C. (eds.) CALCO 2011. LNCS, vol. 6859, pp. 314–328. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  26. 26.
    TeReSe (ed.): Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science, vol. 55. Cambridge University Press (2003)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Kokichi Futatsugi
    • 1
  1. 1.Research Center for Software Verification (RCSV)Japan Advanced Institute of Science and Technology (JAIST)NomiJapan

Personalised recommendations