Qualitative and Quantitative Monitoring of Spatio-Temporal Properties

We present Signal Spatio-Temporal Logic (SSTL), a modal logic that can be used to specify spatio-temporal properties in linear time and for a discrete space. The logic is equipped with a Boolean and a quantitative semantics, and with accompanying monitoring algorithms. As such, it is suitable for real-time verification of both white box and black box complex systems. It can also be integrated into stochastic model checking routines. The logic combines the until temporal modality with two spatial modalities, one expressing that something is true somewhere nearby and the other capturing the notion of being surrounded by a region with a given property. The monitoring algorithms are implemented in an open source Java tool. In the paper we present the logic at work to analyse the formation of patterns in a Turing reaction-diffusion system.