P-hardness of the emptiness problem for visibly pushdown languages

Visibly pushdown languages form a subclass of the context-free languages which is appealing because of its nice algorithmic and closure properties. Here we show that the emptiness problem for this class is not any easier than the emptiness problem for context-free languages, namely hard for deterministic polynomial time. The proof consists of a reduction from the alternating graph reachability problem.

Research highlights► We consider visibly pushdown languages. ► We examine the complexity of their emptiness problem. ► We prove P-hardness of this problem.