Timed Büchi automata provide a very expressive formalism for expressing requirements of real-time systems. Online monitoring and active testing of embedded real-time systems can then be achieved by symbolic execution of such automata on the trace observed from the system. However, this direct construction is only faithful if the observation of the trace is immediate in the sense that the monitor (or test harness, respectively) can assign exact timestamps to the actions it observes. This is rarely true in practice due to the substantial and fluctuating parametric delays introduced by the circuitry connecting the observed system to its monitoring or testing device. We present purely zone-based online monitoring and testing algorithms, which handle such parametric delays exactly without recurrence to costly verification procedures for parametric timed automata. We have implemented our algorithms on top of the real-time model checking tool Uppaal , and report on encouraging initial results.

Abstract In this paper we study monitoring of real-time systems with respect to properties given by a pair of Timed Büchi Automata, one for the property and one for its complement. This includes properties expressible in temporal logics that are closed under complementation and can be translated into Timed Büchi Automata, e.g., Metric Interval Temporal Logic. We introduce efficient symbolic online monitoring algorithms in a number of settings, using difference bound matrices representing zones. Our contributions include a principled treatment of time divergence and monitoring under timing uncertainty. Our online monitoring procedure is implemented in the tool MoniTAal , and shown to effectively monitor properties over long traces.

Monitoring is an important part of the verification toolbox, in particular in situations where exhaustive verification using, e.g., model-checking is infeasible. The goal of online monitoring is to determine the satisfaction or violation of a specification during runtime, i.e., based on finite execution prefixes. However, not every specification is amenable to monitoring, e.g., properties for which no finite execution can witness satisfaction or violation. Monitorability is the question of whether a given specification is amenable to monitoring, and has been extensively studied in discrete time. Here, we study the monitorability problem for real-time properties expressed as Timed Automata. For specifications given by deterministic Timed Muller Automata, we prove decidability while we show that the problem is undecidable for specifications given by nondeterministic Timed Büchi automata. Furthermore, we refine monitorability to also determine bounds on the number of events as well as the time that must pass before monitoring the property may yield an informative verdict. We prove that for deterministic Timed Muller automata, such bounds can be effectively computed. In contrast we show that for nondeterministic Timed Büchi automata such bounds are not computable.