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On the Membership Problem for Visibly Pushdown Languages

  • Conference paper
Automated Technology for Verification and Analysis (ATVA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 4218))

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Abstract

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.

Work partially supported by funds for the research from MIUR 2006, grant “Metodi Formali per la verifica di sistemi chiusi ed aperti”, Università di Salerno.

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Authors and Affiliations

  1. Facoltà di Scienze Matematiche, Fisiche e Naturali, Università degli Studi di Salerno, Italy

    Salvatore La Torre, Margherita Napoli & Mimmo Parente

Authors
  1. Salvatore La Torre
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  2. Margherita Napoli
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  3. Mimmo Parente
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Editors and Affiliations

  1. VERIMAG, 2 Avenue de Vignate, Centre Equitation, 38610, Grenoble-Gières, France

    Susanne Graf

  2. Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Wenhui Zhang

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La Torre, S., Napoli, M., Parente, M. (2006). On the Membership Problem for Visibly Pushdown Languages. In: Graf, S., Zhang, W. (eds) Automated Technology for Verification and Analysis. ATVA 2006. Lecture Notes in Computer Science, vol 4218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11901914_10

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  • DOI: https://doi.org/10.1007/11901914_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-47237-7

  • Online ISBN: 978-3-540-47238-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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