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.