Congruences for Visibly Pushdown Languages

  • Rajeev Alur
  • Viraj Kumar
  • P. Madhusudan
  • Mahesh Viswanathan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3580)


We study congruences on words in order to characterize the class of visibly pushdown languages (Vpl), a subclass of context-free languages. For any language L, we define a natural congruence on words that resembles the syntactic congruence for regular languages, such that this congruence is of finite index if, and only if, L is a Vpl. We then study the problem of finding canonical minimal deterministic automata for Vpls. Though Vpls in general do not have unique minimal automata, we consider a subclass of VPAs called k-module single-entry VPAs that correspond to programs with recursive procedures without input parameters, and show that the class of well-matched Vpls do indeed have unique minimal k-module single-entry automata. We also give a polynomial time algorithm that minimizes such k-module single-entry VPAs.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Rajeev Alur
    • 1
  • Viraj Kumar
    • 2
  • P. Madhusudan
    • 2
  • Mahesh Viswanathan
    • 2
  1. 1.University of PennsylvaniaPhiladelphiaUSA
  2. 2.University of Illinois at Urbana-ChampaignUrbanaUSA

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