2-Visibly Pushdown Automata

  • Dario Carotenuto
  • Aniello Murano
  • Adriano Peron
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4588)


Visibly Pushdown Automata (VPA) are a special case of pushdown machines where the stack operations are driven by the input. In this paper, we consider VPA with two stacks, namely 2-VPA. These automata introduce a useful model to effectively describe concurrent pushdown systems using a simple communication mechanism between stacks. We show that 2-VPA are strictly more expressive than VPA. Indeed, 2-VPA accept some context-sensitive languages that are not context-free and some context-free languages that are not accepted by any VPA. Nevertheless, the class of languages accepted by 2-VPA is closed under all boolean operations and determinizable in ExpTime, but does not preserve decidability of emptiness problem. By adding an ordering constraint on stacks (2-OVPA), decidability of emptiness can be recovered (preserving desirable closure properties) and solved in PTime. Using these properties along with the automata-theoretic approach, we prove that the model checking problem over 2-OVPA models against 2-OVPA specifications is ExpTime-complete.


Model Check Input Symbol Model Check Problem Pushdown Automaton Push Transition 
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.
    Alur, R., Madhusudan, P.: Visibly pushdown languages. In: STOC 2004, pp. 202–211. ACM Press, New York (2004)CrossRefGoogle Scholar
  2. 2.
    Bozzelli, L., Murano, A., Peron, A.: Pushdown module checking. In: Sutcliffe, G., Voronkov, A. (eds.) LPAR 2005. LNCS (LNAI), vol. 3835, pp. 504–518. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Breveglieri, L., Cherubini, A., Citrini, C., Crespi-Reghizzi, S.: Multi-push-down languages and grammars. Int. J. Found. Comput. Sci. 7(3), 253–292 (1996)zbMATHCrossRefGoogle Scholar
  4. 4.
    Clarke, E.M., Emerson, E.A.: Design and verification of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) Logics of Programs. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982)CrossRefGoogle Scholar
  5. 5.
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
  6. 6.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)zbMATHGoogle Scholar
  7. 7.
    Kupferman, O., Piterman, N., Vardi, M.: Pushdown specifications. In: Baaz, M., Voronkov, A. (eds.) LPAR 2002. LNCS (LNAI), vol. 2514, pp. 262–277. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)zbMATHGoogle Scholar
  9. 9.
    Queille, J.P., Sifakis, J.: Specification and verification of concurrent programs in Cesar. In: Dezani-Ciancaglini, M., Montanari, U. (eds.) International Symposium on Programming. LNCS, vol. 137, pp. 337–351. Springer, Heidelberg (1981)Google Scholar
  10. 10.
    Sistla, A., Clarke, E.M., Francez, N., Gurevich, Y.: Can message buffers be axiomatized in linear temporal logic. Information and Control 63(1-2), 88–112 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Van Steen, M., Tanenbaum, A.S.: Distributed Systems: Principles and Paradigms. Prentice Hall, Englewood Cliffs (2002)Google Scholar
  12. 12.
    Vardi, M.Y., Wolper, P.: Automata-theoretic techniques for modal logics of programs. J. of Computer and System Sciences 32(2), 182–221 (1986)CrossRefMathSciNetGoogle Scholar
  13. 13.
    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 2007

Authors and Affiliations

  • Dario Carotenuto
    • 1
  • Aniello Murano
    • 1
  • Adriano Peron
    • 1
  1. 1.Università degli Studi di Napoli “Federico II”, Via Cinthia, I-80126 NapoliItaly

Personalised recommendations