Right-Universality of Visibly Pushdown Automata

Abstract

Visibly pushdown automata (VPAs) express properties on structures with a nesting relation such as program traces with nested method calls. In the context of runtime verification, we are interested in the following problem: given u, the beginning of a program trace, and A, a VPA expressing a property to be checked on this trace, can we ensure that any extension uv of u will be accepted by A? We call this property right-universality w.r.t. u. We propose an online algorithm detecting at the earliest position of the trace, whether this trace is accepted by A. The decision problem associated with right-universality is ExpTime-complete. Our algorithm uses antichains and other optimizations, in order to avoid the exponential blow-up in most cases. This is confirmed by promising experiments conducted on a prototype implementation.