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From biological systems to cyber-physical systems, monitoring the behavior of such dynamical systems often requires to reason about complex spatio-temporal properties of physical and/or computational entities that are dynamically interconnected and arranged in a particular spatial configuration. Spatio-Temporal Reach and Escape Logic (STREL) is a recent logic-based formal language designed to specify and to reason about spatio-temporal properties. STREL considers each system's entity as a node of a dynamic weighted graph representing their spatial arrangement. Each node generates a set of mixed-analog signals describing the evolution over time of computational and physical quantities characterising the node's behavior. While there are offline algorithms available for monitoring STREL specifications over logged simulation traces, here we investigate for the first time an online algorithm enabling the runtime verification during the system's execution or simulation. Our approach extends the original framework by considering imprecise signals and by enhancing the logics' semantics with the possibility to express partial guarantees about the conformance of the system's behavior with its specification. Finally, we demonstrate our approach in a real-world environmental monitoring case study. CCS CONCEPTS• Theory of computation → Logic and verification; Modal and temporal logics; • Software and its engineering → Abstraction, modeling and modularity.

Engineering cyber-physical systems inhabiting contemporary urban spatial environments demands software engineering facilities to support design and operation. Tools and approaches in civil engineering and architectural informatics produce artifacts that are geometrical or geographical representations describing physical spaces. The models we consider conform to the CityGML standard; although relying on international standards and accessible in machine-readable formats, such physical space descriptions often lack semantic information that can be used to support analyses. In our context, analysis as commonly understood in software engineering refers to reasoning on properties of an abstracted model—in this case a city design. We support model-based development, firstly by providing a way to derive analyzable models from CityGML descriptions, and secondly, we ensure that changes performed are propagated correctly. Essentially, a digital twin of a city is kept synchronized, in both directions, with the information from the actual city. Specifically, our formal programming technique and accompanying technical framework assure that relevant information added, or changes applied to the domain (resp. analyzable) model are reflected back in the analyzable (resp. domain) model automatically and coherently. The technique developed is rooted in the theory of bidirectional transformations, which guarantees that synchronization between models is consistent and well behaved. Produced models can bootstrap graph-theoretic, spatial or dynamic analyses. We demonstrate that bidirectional transformations can be achieved in practice on real city models.

We propose an interdisciplinary framework, Bayesian formal predictive model checking (Bayes FPMC), which combines Bayesian predictive inference, a well established tool in statistics, with formal verification methods rooting in the computer science community.Bayesian predictive inference allows for coherently incorporating uncertainty about unknown quantities by making use of methods or models that produce predictive distributions which in turn inform decision problems. By formalizing these problems and the corresponding properties, we can use spatio-temporal reach and escape logic to probabilistically assess their satisfaction. This way, competing models can directly be ranked according to how well they solve the actual problem at hand. The approach is illustrated on an urban mobility application, where the crowdedness in the center of Milan is proxied by aggregated mobile phone traffic data. We specify several desirable spatio-temporal properties related to city crowdedness such as a fault tolerant network or the reachability of hospitals. After verifying these properties on draws from the posterior predictive distributions, we compare several spatio-temporal Bayesian models based on their overall and property-based predictive performance.