Visibly Pushdown Automata: Universality and Inclusion via Antichains

Visibly pushdown automata (VPAs), introduced by Alur and Madhusudan in 2004, are a useful formalism in various contexts, such as expressing and checking properties on control flows of programs, or on XML documents. In this context, we propose efficient antichain-based algorithms to check universality and inclusion of VPAs. Whereas the computation complexity is known to be ExpTime-complete for both problems, we show how antichains can avoid explicit determinization and save computations. The approach is extended to hedge automata. We implement the proposed algorithms in a prototype tool and conduct experiments on randomly generated VPAs. We show that, on numerous instances, our algorithms outperform other VPA tools.