Minimizing Variants of Visibly Pushdown Automata

  • Patrick Chervet
  • Igor Walukiewicz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4708)

Abstract

The minimization problem for visibly pushdown automata (VPA) is studied. Two subclasses of VPA are introduced: call driven automata, and block automata. For the first class, minimization results are given unifying and generalizing those present in the literature. Unfortunately, this class shares the drawback of all other classes for which a minimization result is known: it is exponentially less succinct than VPA. The second class, block automata, is introduced to address this problem. These automata are as succinct as VPA. A minimization procedure for them is presented that requires one additional parameter to be fixed. An example of an exponential gain in succinctness is given.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alur, R., Etessami, K., Madhusudan, P.: A temporal logic of nested calls and returns. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 467–481. Springer, Heidelberg (2004)Google Scholar
  2. 2.
    Alur, R., Kumar, V., Madhusudan, P., Viswanathan, M.: Congruences for visibly pushdown languages. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1102–1114. Springer, Heidelberg (2005)Google Scholar
  3. 3.
    Alur, R., Kumar, V., Madhusudan, P., Viswanathan, M.: Congruences for visibly pushdown languages. Technical Report UIUCDCS-R-2005 -2565, UIUC, Technical report (2005)Google Scholar
  4. 4.
    Alur, R., Madhusudan, P.: Visibly pushdown languages. In: Proceedings of STOC, pp. 202–211. ACM Press, New York (2004)Google Scholar
  5. 5.
    Berstel, J., Boasson, L.: Balanced grammars and their languages. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds.) Formal and Natural Computing. LNCS, vol. 2300, pp. 419–426. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Dill, D.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) Automatic Verification Methods for Finite State Systems. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990)Google Scholar
  7. 7.
    Kumar, V., Madhusdan, P., Viswanathan, M.: Visibly pushdown automata for streaming XML. In: Proceedings of WWW, pp. 1053–1062. ACM Press, New York (2007)Google Scholar
  8. 8.
    Kumar, V., Madhusudan, P., Viswanathan, M.: Minimization, learning, and conformance testing of boolean programs. In: Baier, C., Hermanns, H. (eds.) CONCUR 2006. LNCS, vol. 4137, pp. 203–217. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Loding, C., Madhusudan, P., Serre, O.: Visibly pushdown games. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, Springer, Heidelberg (2004)Google Scholar
  10. 10.
    McNaughton, R.: Parenthesis grammars. Journal of the ACM 14, 490–650 (1967)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Mehlhorn, K.: Pebbling mountain ranges and its application of dcfl-recognition. In: de Bakker, J.W., van Leeuwen, J. (eds.) Automata, Languages and Programming. LNCS, vol. 85, pp. 422–435. Springer, Heidelberg (1980)Google Scholar
  12. 12.
    Michon, J-F., Champarnaud, J.-F.: Automata and binary decision diagrams. In: Champarnaud, J.-M., Maurel, D., Ziadi, D. (eds.) WIA 1998. LNCS, vol. 1660, pp. 742–746. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  13. 13.
    Murawski, A., Walukiewicz, I.: Third-order idealized algol with iteration is decidable. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 202–218. Springer, Heidelberg (2005)Google Scholar
  14. 14.
    Chervet, P., Walukiewicz, I.: Minimizing variants of visibly pushdown automata (2007), http://www.labri.fr/perso/igw/publications.html
  15. 15.
    Pitcher, C.: Visibly pushdown expression effects for XML streem processing. In: Programming Language Techonologies for XML, pp. 1–14 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Patrick Chervet
    • 1
  • Igor Walukiewicz
    • 1
  1. 1.LaBRI, Université de Bordeaux and CNRS, 351, Cours de la Libération, F-33 405, Talence cedexFrance

Personalised recommendations