Ramsey Goes Visibly Pushdown

Abstract

Checking whether one formal language is included in another is vital to many verification tasks. In this paper, we provide solutions for checking the inclusion of the languages given by visibly pushdown automata over both finite and infinite words. Visibly pushdown automata are a richer automaton model than the classical finite-state automata, which allows one, e.g., to reason about the nesting of procedure calls in the executions of recursive imperative programs. The highlight of our solutions is that they do not comprise automata constructions for determinization and complementation. Instead, our solutions are more direct and generalize the so-called Ramsey-based inclusion-checking algorithms, which apply to classical finite-state automata and proved effective there, to visibly pushdown automata. We also experimentally evaluate our algorithms thereby demonstrating the virtues of avoiding determinization and complementation constructions.