The word problem for visibly pushdown languages described by grammars

  • Authors:

  • Salvatore Torre;Margherita Napoli;Mimmo Parente

  • Affiliations:

  • Dipartimento di Informatica ed Applicazioni, Università degli Studi di Salerno, Fisciano, Italy 84084;Dipartimento di Informatica ed Applicazioni, Università degli Studi di Salerno, Fisciano, Italy 84084;Dipartimento di Informatica ed Applicazioni, Università degli Studi di Salerno, Fisciano, Italy 84084

  • Venue:
  • Formal Methods in System Design
  • Year:
  • 2007

  • Pumping visibly pushdown languages

    AIASABEBI'11 Proceedings of the 11th WSEAS international conference on Applied informatics and communications, and Proceedings of the 4th WSEAS International conference on Biomedical electronics and biomedical informatics, and Proceedings of the international conference on Computational engineering in systems applications

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Abstract

Visibly pushdown languages are an interesting subclass of deterministic context-free languages that can model nonregular properties of interest in program analysis. Such class properly contains typical classes of parenthesized languages such as "parenthesis", "bracketed", "balanced" and "input-driven" languages. It is closed under boolean operations and has decidable decision problems such as emptiness, inclusion and universality. We study the membership problem for visibly pushdown languages, and show that it can be solved in time linear in both the size of the input grammar and the length of the input word. The algorithm relies on a reduction to the reachability problem for game graphs. We also discuss the time complexity of the membership problem for the class of balanced languages which is the largest among those cited above. Besides the intrinsic theoretical interest, we further motivate our main result showing an application to the validation of XML documents against Schema and Document Type Definitions (DTDs).