The reachability analysis of weighted pushdown systems is a very powerful technique in verification and analysis of recursive programs. Each transition rule of a weighted pushdown system is associated with an element of a bounded semiring representing the weight of the rule. However, we have realized that the restriction of the boundedness is too strict and the formulation of weighted pushdown systems is not general enough for some applications.

To generalize weighted pushdown systems, we first introduce the notion of stack signatures that summarize the effect of a computation of a pushdown system and formulate pushdown systems as automata over the monoid of stack signatures. We then generalize weighted pushdown systems by introducing semirings indexed by the monoid and weaken the boundedness to local boundedness.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BEM97]
    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)CrossRefGoogle Scholar
  2. [Eil74]
    Eilenberg, S.: Automata, Languages, and Machines, vol. A. Academic Press (1974)Google Scholar
  3. [ÉK09]
    Ésik, Z., Kuich, W.: Finite automata. In: Droste, M., Kuich, W., Vogler, H. (eds.) Handbook of Weighted Automata, ch. 3, pp. 69–104. Springer (2009)Google Scholar
  4. [EKS03]
    Esparza, J., Kucera, A., Schwoon, S.: Model checking LTL with regular valuations for pushdown systems. Information and Computation 186(2), 355–376 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  5. [FWW97]
    Finkel, A., Willems, B., Wolper, P.: A direct symbolic approach to model checking pushdown systems. In: INFINITY 1997. ENTCS, vol. 9, pp. 27–39 (1997)Google Scholar
  6. [LO10]
    Li, X., Ogawa, M.: Conditional weighted pushdown systems and applications. In: Proceedings of the 2010 ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation, pp. 141–150 (2010)Google Scholar
  7. [Min07]
    Minamide, Y.: Verified Decision Procedures on Context-Free Grammars. In: Schneider, K., Brandt, J. (eds.) TPHOLs 2007. LNCS, vol. 4732, pp. 173–188. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. [MM12]
    Minamide, Y., Mori, S.: Reachability Analysis of the HTML5 Parser Specification and Its Application to Compatibility Testing. In: Giannakopoulou, D., Méry, D. (eds.) FM 2012. LNCS, vol. 7436, pp. 293–307. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  9. [MT06]
    Minamide, Y., Tozawa, A.: XML Validation for Context-Free Grammars. In: Kobayashi, N. (ed.) APLAS 2006. LNCS, vol. 4279, pp. 357–373. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. [RSJM05]
    Reps, T., Schwoon, S., Jha, S., Melski, D.: Weighted pushdown systems and their application to interprocedural dataflow analysis. Science of Computer Programming 58, 206–263 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  11. [Sak09]
    Sakarovitch, J.: Elements of Automata Theory. Cambridge University Press (2009)Google Scholar
  12. [Sha67]
    Shamir, E.: A representation theorem for algebraic and context-free power series in non commuting variables. Information and Control 11(1/2), 239–254 (1967)MathSciNetzbMATHCrossRefGoogle Scholar
  13. [Suw09]
    Suwimonteerabuth, D.: Reachability in Pushdown Systems: Algorithms and Applications. PhD thesis, Technischen Universität München (2009)Google Scholar
  14. [TM07]
    Tozawa, A., Minamide, Y.: Complexity Results on Balanced Context-Free Languages. In: Seidl, H. (ed.) FOSSACS 2007. LNCS, vol. 4423, pp. 346–360. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yasuhiko Minamide
    • 1
  1. 1.Faculty of Engineering, Information and SystemsUniversity of TsukubaJapan

Personalised recommendations