On the Membership Problem for Visibly Pushdown Languages

  • Salvatore La Torre
  • Margherita Napoli
  • Mimmo Parente
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4218)


Visibly pushdown languages are a subclass of deterministic context-free languages that can model nonregular properties of interest in program analysis. This class properly contains typical classes of parenthesized languages like “balanced” and “input-driven” languages. Visibly pushdown languages are closed under boolean operations and some decision problems, such as inclusion and universality, are decidable. In this paper, we study the membership problem for this class of languages and show that it can be solved in time linear in the size of the input grammar and in the length of the input word. The algorithm consists of a reduction to the reachability problem on game graphs. The same approach can be efficiently applied when the input language is given as a visibly pushdown automaton, moreover we also show time complexities of the same problem using other approaches. We further motivate our result showing an application to XML schema.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Salvatore La Torre
    • 1
  • Margherita Napoli
    • 1
  • Mimmo Parente
    • 1
  1. 1.Facoltà di Scienze Matematiche, Fisiche e NaturaliUniversità degli Studi di SalernoItaly

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