Compositional Failure Detection in Structured Transition Systems

  • Ingo Felscher
  • Wolfgang Thomas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6807)


In model-checking, systems are often given as products. We propose an approach that is built on a preprocessing of specifications in terms of appropriate automata. This allows to incorporate information about the local behaviour and synchronization of the system components into the specification. We develop a framework of (partially) synchronized automaton products and a format of corresponding specification automata that allows for a compositional failure detection of linear regular properties (either for finite or for infinite behaviour). As a result we obtain an algorithm which separates the local and the non-local segments of system runs, resulting in improved complexity bounds in typical specifications.


model-checking finitely synchronized products compositional failure detection 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Addison Wesley, Reading (1974)MATHGoogle Scholar
  2. 2.
    Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press, Cambridge (2008)MATHGoogle Scholar
  3. 3.
    Bodentien, N.O., Vestergaard, J., Friis, J., Kristoffersen, K.J., Larsen, K.G.: Verification of state/event systems by quotienting. BRICS RS-99-41 (December 1999) Nordic Workshop in Programming Theory, Uppsala, Sweden, October 6–8 (1999)Google Scholar
  4. 4.
    Büchi, J.R.: Weak second-order arithmetic and finite automata. Zeitschrift für Mathematische Logik und Grundladen Der Mathematik 6, 66–92 (1960)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Chang, C.C., Keisler, H.J.: Model Theory. North Holland, Amsterdam (1990)MATHGoogle Scholar
  6. 6.
    Cheung, S.C., Kramer, J.: Context constraints for compositional reachability analysis. ACM Trans. Softw. Eng. Methodol. 5, 334–377 (1996)CrossRefGoogle Scholar
  7. 7.
    Dawar, A., Grohe, M., Kreutzer, S., Schweikardt, N.: Model theory makes formulas large. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 913–924. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Elgot, C.: Decision problems of finite automata design and related arithmetics. Transactions of the American Mathematical Society 98, 2152 (1961)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Feferman, S., Vaught, R.: The first-order properties of products of algebraic systems. Fundamenta Mathematicae 47, 57–103 (1959)MathSciNetMATHGoogle Scholar
  10. 10.
    Felscher, I.: The compositional method and regular reachability. Electronic Notes in Theoretical Computer Science 223, 103–117 (2008)CrossRefMATHGoogle Scholar
  11. 11.
    Felscher, I., Thomas, W.: On compositional failure detection in structured transition systems, RWTH Aachen Unviersity, Department of Computer Science, Tech. Rep.AIB-2011-12Google Scholar
  12. 12.
    Gabbay, D., Shehtman, V.: Products of modal logics. Logic Journal of IGPL 6(1), 73–146 (1998)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Hodges, W.: Model theory, Encyclopedia of Mathematics and its Applications, vol. 42. Cambridge University Press, Cambridge (1993)Google Scholar
  14. 14.
    Makowsky, J.A.: Algorithmic uses of the feferman-vaught theorem. Annals of Pure and Applied Logic 126(1-3), 159–213 (2004)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Mostowski, A.: On direct products of theories. The Journal of Symbolic Logic 17(1), 1–31 (1952)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Rabinovich, A.: On compositionality and its limitations. ACM Transactions on Computational Logic 8(1) (January 2007)Google Scholar
  17. 17.
    Shelah, S.: The monadic theory of order. The Annals of Mathematics 102(3), 379–419 (1975)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Thomas, W.: Ehrenfeucht games, the composition method, and the monadic theory of ordinal words. In: Mycielski, J., Rozenberg, G., Salomaa, A. (eds.) Structures in Logic and Computer Science. LNCS, vol. 1261, pp. 118–143. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  19. 19.
    Thomas, W.: Languages, automata and logic. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, Beyond Words, vol. 3, pp. 389–455. Springer, New York (1997)CrossRefGoogle Scholar
  20. 20.
    Wöhrle, S., Thomas, W.: Model checking synchronized products of infinite transition systems. In: Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science. LNCS, pp. 2–11. IEEE Computer Society Press, Los Alamitos (2004)Google Scholar
  21. 21.
    Wolper, P.: Constructing automata from temporal logic formulas: A tutorial. In: Brinksma, E., Hermanns, H., Katoen, J.-P. (eds.) EEF School 2000 and FMPA 2000. LNCS, vol. 2090, pp. 261–277. Springer, Heidelberg (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ingo Felscher
    • 1
  • Wolfgang Thomas
    • 1
  1. 1.RWTH Aachen UniversityGermany

Personalised recommendations