Congruences for visibly pushdown languages

  • Authors:

  • Rajeev Alur;Viraj Kumar;P. Madhusudan;Mahesh Viswanathan

  • Affiliations:

  • University of Pennsylvania, Philadelphia, PA;University of Illinois at Urbana-Champaign, Urbana, IL;University of Illinois at Urbana-Champaign, Urbana, IL;University of Illinois at Urbana-Champaign, Urbana, IL

  • Venue:
  • ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
  • Year:
  • 2005

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Abstract

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.