Runtime Monitoring of Metric First-order Temporal Properties

We introduce a novel approach to the runtime monitoring of complex system properties. In particular, we present an online algorithm for a safety fragment of metric first-order temporal logic that is considerably more expressive than the logics supported by prior monitoring methods. Our approach, based on automatic structures, allows the unrestricted use of negation, universal and existential quantification over infinite domains, and the arbitrary nesting of both past and bounded future operators. Moreover, we show how to optimize our approach for the common case where structures consist of only finite relations, over possibly infinite domains. Under an additional restriction, we prove that the space consumed by our monitor is polynomially bounded by the cardinality of the data appearing in the processed prefix of the temporal structure being monitored