Model Checking for Process Rewrite Systems and a Class of Action-Based Regular Properties

  • Laura Bozzelli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3385)


We consider the model checking problem for Process Rewrite Systems (PRSs), an infinite-state formalism (non Turing-powerful) which subsumes many common models such as Pushdown Processes and Petri Nets. PRSs can be adopted as formal models for programs with dynamic creation and synchronization of concurrent processes, and with recursive procedures. The model-checking problem for PRSs w.r.t. action-based linear temporal logic (ALTL) is undecidable. However, decidability for some interesting fragment of ALTL remains an open question. In this paper we state decidability results concerning generalized acceptance properties about infinite derivations (infinite term rewriting) in PRSs. As a consequence, we obtain decidability of the model-checking (restricted to infinite runs) for PRSs and a meaningful fragment of ALTL.


Normal Form Model Check Label Transition System Reachability Analysis Rule 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.
    Bouajjani, A., Habermehl, P.: Constrained Properties, Semilinear Systems, and Petri Nets. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 481–497. Springer, Heidelberg (1996)Google Scholar
  2. 2.
    Bouajjani, A., Esparza, J., Maler, O.: Reachability Analysis of Pushdown Automata: Application to Model-Checking. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 135–150. Springer, Heidelberg (1997)Google Scholar
  3. 3.
    Bouajjani, A., Touili, T.: Reachability Analysis of Process Rewrite Systems. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 74–87. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Burkart, O., Steffen, B.: Pushdown Processes: Parallel Composition and Model Checking. In: Jonsson, B., Parrow, J. (eds.) CONCUR 1994. LNCS, vol. 836, pp. 98–113. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  5. 5.
    Burkart, O., Caucal, D., Moller, F., Steffen, B.: Verification on Infinite Structures. In: Handbook of Process Algebra, pp. 545–623. North-Holland, Amsterdam (2001)CrossRefGoogle Scholar
  6. 6.
    Davis, M.D., Weyuker, E.J.: Computability, Complexity, and Languages, pp. 47–49. Academic Press, London (1983)zbMATHGoogle Scholar
  7. 7.
    Emerson, E.A., Halpern, J.Y.: “Sometimes” and “Not Never” Revisited: On Branching Versus Linear Time. In: POPL 1983, pp. 127–140 (1983)Google Scholar
  8. 8.
    Esparza, J.: On the Decidability of Model Checking for Several μ-calculi and Petri Nets. In: Tison, S. (ed.) CAAP 1994. LNCS, vol. 787, pp. 115–129. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  9. 9.
    Esparza, J.: Decidability of Model Checking for Infinite–State Concurrent Systems. Acta Informaticae 34(2), 85–107 (1997)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Esparza, J., Hansel, D., Rossmanith, P., Schwoon, S.: Efficient Algorithms for Model Checking Pushdown Systems. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 232–247. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  11. 11.
    Habermehl, P.: On the complexity of the linear-time mu-calculus for Petri nets. In: Azéma, P., Balbo, G. (eds.) ICATPN 1997. LNCS, vol. 1248, pp. 102–116. Springer, Heidelberg (1997)Google Scholar
  12. 12.
    Mayr, R.: Decidability and Complexity of Model Checking Problems for Infinite- State Systems.PhD. thesis, Techn. Univ. of Munich (1998)Google Scholar
  13. 13.
    Mayr, R.: Process Rewrite Systems. Information and Computation 156, 264–286 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Walukiewicz, I.: Pushdown processes: Games and Model Checking. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 62–74. Springer, Heidelberg (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Laura Bozzelli
    • 1
  1. 1.Dipartimento di Matematica e ApplicazioniUniversità di Napoli “Federico II”NapoliItaly

Personalised recommendations