The Surprising Robustness of (Closed) Timed Automata against Clock-Drift

We investigate reachability (or equivalently, safety) for timed systems modelled as Timed Automata (TA) under notions of “robustness”, i.e., when the clocks of the TA may drift by small amounts. Our contributions are two-fold: (1) We first consider the model of clock-drift introduced by Puri [1] and subsequently studied in other works [2, 3, 4]. We show that the standard zone-based forward reachability analysis performed by tools such as UPPAAL is in fact exact for TA with closed guards, invariants, and targets, when testing robust safety of timed systems having an arbitrary, but finite lifetime. (2) Next, we consider a more realistic model of drifting clocks that takes into account the regular resynchronization performed in most practical systems. We then show that the standard reachability analysis of tools like UPPAAL again suffices to test for robust safety in this model of clock-drift, for TA with closed guards, invariants, and targets, but now without any restrictions on system life-time.