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Cyber-Physical Systems (CPS) consist of inter-wined computational (cyber) and physical components interacting through sensors and/or actuators. Computational elements are networked at every scale and can communicate with each other and with humans. Nodes can join and leave the network at any time or they can move to different spatial locations. In this scenario, monitoring spatial and temporal properties plays a key role in the understanding of how complex behaviors can emerge from local and dynamic interactions. We revisit here the Spatio-Temporal Reach and Escape Logic (STREL), a logic-based formal language designed to express and monitor spatio-temporal requirements over the execution of mobile and spatially distributed CPS. STREL considers the physical space in which CPS entities (nodes of the graph) are arranged as a weighted graph representing their dynamic topological configuration. Both nodes and edges include attributes modeling physical and logical quantities that can evolve over time. STREL combines the Signal Temporal Logic with two spatial modalities reach and escape that operate over the weighted graph. From these basic operators, we can derive other important spatial modalities such as everywhere, somewhere and surround. We propose both qualitative and quantitative semantics based on constraint semiring algebraic structure. We provide an offline monitoring algorithm for STREL and we show the feasibility of our approach with the application to two case studies: monitoring spatio-temporal requirements over a simulated mobile ad-hoc sensor network and a simulated epidemic spreading model for COVID19., Comment: arXiv admin note: substantial text overlap with arXiv:1904.08847

In spatially located, large scale systems, time and space dynamics interact and drives the behaviour. Examples of such systems can be found in many smart city applications and Cyber-Physical Systems. In this paper we present the Signal Spatio-Temporal Logic (SSTL), a modal logic that can be used to specify spatio-temporal properties of linear time and discrete space models. The logic is equipped with a Boolean and a quantitative semantics for which efficient monitoring algorithms have been developed. As such, it is suitable for real-time verification of both white box and black box complex systems. These algorithms can also be combined with stochastic model checking routines. SSTL 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 that satisfies a given spatio-temporal property. The monitoring algorithms are implemented in an open source Java tool. We illustrate the use of SSTL analysing the formation of patterns in a Turing Reaction-Diffusion system and spatio-temporal aspects of a large bike-sharing system., Comment: 36 pages with 13 figures