Qualitative and Quantitative Monitoring of Spatio-Temporal Properties

Abstract

Abstract. We address the specification and verification of spatio-temporal behaviours of complex systems, introducing Signal Spatio-Temporal Logic (SSTL). This modal logic extends the Signal Temporal Logic with spatial operators capable of specifying topological properties in a discrete space. The latter is modelled as a weighted graph, and provided with a boolean and a quantitative semantics. Furthermore, we define efficient monitoring algorithms for both the boolean and the quantitative semantics. These are implemented in a Java tool available online. We illustrate the expressiveness of SSTL and the effectiveness of the monitoring procedures on the formation of patterns in a Turing reaction-diffusion system.

Studying Emergent Behaviours in Morphogenesis Using Signal Spatio-Temporal Logic

“…The Signal Spatio-Temporal Logic (SSTL) [10,24] is a linear time logic suitable to specify spatio-temporal behaviours of traces generated from simulations. It is an extension of Signal Temporal Logic (STL) [23] with two spatial modalities.…”

“…SSTL is equipped with efficient monitoring algorithms for both the boolean and the quantitative semantics, whose description, together with a formalisation of the semantics, can be found in [10,24].…”

“…In the last year, two novel spatio-temporal logics, SpaTeL [18] and SSTL [10,24] have made their appearance almost at the same time in the realm of formal methods to specify the emergence of spatio-temporal patterns.…”

“…The Signal Spatio-Temporal Logic (SSTL) [10,24] is the extension of STL [23] with three spatial modalities, somewhere, everywhere and surround, which can be nested arbitrarily with the original STL temporal operator. In [10,24], the authors provide a qualitative and quantitative semantics of SSTL and efficient monitoring algorithms for both semantics.…”

“…In [10,24], the authors provide a qualitative and quantitative semantics of SSTL and efficient monitoring algorithms for both semantics. A more detailed description of SSTL is provided in Section 3.…”