On the membership problem for visibly pushdown languages

Authors:
Salvatore La Torre;Margherita Napoli;Mimmo Parente
Affiliations:
Facoltà di Scienze Matematiche, Fisiche e Naturali, Università degli Studi di Salerno, Italy;Facoltà di Scienze Matematiche, Fisiche e Naturali, Università degli Studi di Salerno, Italy;Facoltà di Scienze Matematiche, Fisiche e Naturali, Università degli Studi di Salerno, Italy
Venue:
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
Year:
2006

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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.