Parameter Invariant Monitoring for Signal Temporal Logic

Abstract

Signal Temporal Logic (STL) is a prominent specification formalism for real-time systems, and monitoring these specifications, specially when (for different reasons such as learning) behavior of systems can change over time, is quite important. There are three main challenges in this area: (1) full observation of system state is not possible due to noise or nuisance parameters, (2) the whole execution is not available during the monitoring, and (3) computational complexity of monitoring continuous time signals is very high. Although, each of these challenges has been addressed by different works, to the best of our knowledge, no one has addressed them all together. In this paper, we show how to extend any parameter invariant test procedure for single points in time to a parameter invariant test procedure for efficiently monitoring continuous time executions of a system against STL properties. We also show, how to extend probabilistic error guarantee of the input test procedure to a probabilistic error guarantee for the constructed test procedure.