Decidability Issues for Extended Ping-Pong Protocols

We use some recent techniques from process algebra to draw several conclusions about the well-studied class of ping-pong protocols introduced by Dolev and Yao. In particular we show that all nontrivial properties, including reachability and equivalence checking wrt. the whole van Glabbeek’s spectrum, become undecidable for a very simple recursive extension of the protocol. The result holds even if no nondeterministic choice operator is allowed, but reachability is shown to be decidable in polynomial time if only two parties are participating in the protocol. We also show that the calculus is capable of an implicit description of the active intruder, including full analysis and synthesis of messages in the sense of Amadio, Lugiez, and Vanackère. We conclude by showing that reachability analysis for a replicative variant of the protocol becomes decidable.