From the formation of traffic jams to the development of troublesome, whirlpool-like spirals in the heart’s electrical activity, spatio-temporal patterns are key in understanding how complex behaviors can emerge in a network of locally interacting dynamical systems. One of the most important and intriguing questions is how to specify spatio-temporal behaviors in a formal and human-understandable specification language and how to monitor their onset efficiently. In this tutorial, we present the spatio-temporal logic STREL and its expressivity to specify and monitor spatio-temporal behaviors over complex dynamical and spatially distributed systems. We demonstrate our formalism’s applicability to different scenarios considering static or dynamic spatial configurations and systems with deterministic or stochastic dynamics.
