The work described in this paper builds on the polyhedral semantics of the Spatial Logic for Closure Spaces (SLCS) and the geometric spatial model checker PolyLogicA. Polyhedral models are central in domains that exploit mesh processing, such as 3D computer graphics. A discrete representation of polyhedral models is given by cell poset models, which are amenable to geometric spatial model checking on polyhedral models using the logical language SLCS$η$, a weaker version of SLCS. In this work we show that the mapping from polyhedral models to cell poset models preserves and reflects SLCS$η$. We also propose weak simplicial bisimilarity on polyhedral models and weak $\pm$-bisimilarity on cell poset models, where by ``weak'' we mean that the relevant equivalence is coarser than the corresponding one for SLCS, leading to a greater reduction of the size of models and thus to more efficient model checking. We show that the proposed bisimilarities enjoy the Hennessy-Milner property, i.e. two points are weakly simplicial bisimilar iff they are logically equivalent for SLCS$η$. Similarly, two cells are weakly $\pm$-bisimilar iff they are logically equivalent in the poset-model interpretation of SLCS$η$. Furthermore we present a model minimisation procedure and prove that it correctly computes the minimal model with respect to weak $\pm$-bisimilarity, i.e. with respect to logical equivalence of SLCS$η$. The procedure works via an encoding into LTSs and then exploits branching bisimilarity on those LTSs, exploiting the minimisation capabilities as included in the mCRL2 toolset. Various examples show the effectiveness of the approach.

Segmentation of 3D medical images, and brain segmentation in particular, is an important topic in neuroimaging and in radiotherapy. Overcoming the current, time consuming, practise of manual delineation of brain tumours and providing an accurate, explainable, and replicable method of segmentation of the tumour area and related tissues is therefore an open research challenge. In this paper, we first propose a novel symbolic approach to brain segmentation and delineation of brain lesions based on spatial model checking. This method has its foundations in the theory of closure spaces, a generalisation of topological spaces, and spatial logics. At its core is a high-level declarative logic language for image analysis, ImgQL, and an efficient spatial model checker, VoxLogicA, exploiting state-of-the-art image analysis libraries in its model checking algorithm. We then illustrate how this technique can be combined with Machine Learning techniques leading to a hybrid AI approach that provides accurate and explainable segmentation results. We show the results of the application of the symbolic approach on several public datasets with 3D magnetic resonance (MR) images. Three datasets are provided by the 2017, 2019 and 2020 international MICCAI BraTS Challenges with 210, 259 and 293 MR images, respectively, and the fourth is the BrainWeb dataset with 20 (synthetic) 3D patient images of the normal brain. We then apply the hybrid AI method to the BraTS 2020 training set. Our segmentation results are shown to be in line with the state-of-the-art with respect to other recent approaches, both from the accuracy point of view as well as from the view of computational efficiency, but with the advantage of them being explainable.

Closure spaces, a generalisation of topological spaces, have shown to be a convenient theoretical framework for spatial model checking. The closure operator of closure spaces and quasi-discrete closure spaces induces a notion of neighborhood akin to that of topological spaces that build on open sets. For closure models and quasi-discrete closure models, in this paper we present three notions of bisimilarity that are logically characterised by corresponding modal logics with spatial modalities: (i) CM-bisimilarity for closure models (CMs) is shown to generalise topo-bisimilarity for topological models and to be an instantiation of neighbourhood bisimilarity, when CMs are seen as (augmented) neighbourhood models. CM-bisimilarity corresponds to equivalence with respect to the infinitary modal logic IML that includes the modality ${\cal N}$ for ``being near to''. (ii) CMC-bisimilarity, with `CMC' standing for CM-bisimilarity with converse, refines CM-bisimilarity for quasi-discrete closure spaces, carriers of quasi-discrete closure models. Quasi-discrete closure models come equipped with two closure operators, Direct ${\cal C}$ and Converse ${\cal C}$, stemming from the binary relation underlying closure and its converse. CMC-bisimilarity, is captured by the infinitary modal logic IMLC including two modalities, Direct ${\cal N}$ and Converse ${\cal N}$, corresponding to the two closure operators. (iii) CoPa-bisimilarity on quasi-discrete closure models, which is weaker than CMC-bisimilarity, is based on the notion of compatible paths. The logical counterpart of CoPa-bisimilarity is the infinitary modal logic ICRL with modalities Direct $ζ$ and Converse $ζ$, whose semantics relies on forward and backward paths, respectively. It is shown that CoPa-bisimilarity for quasi-discrete closure models relates to divergence-blind stuttering equivalence for Kripke models.

Abstract We present an application of strategy synthesis to enforce spatial properties. This is achieved by implementing a toolchain that enables the tools and to interact in a fully automated way. The Contract Automata Library () is aimed at both composition and strategy synthesis of games modelled in a dialect of finite state automata. The Voxel-based Logical Analyser () is a spatial model checker for the verification of properties expressed using the Spatial Logic of Closure Spaces on pixels of digital images. We provide examples of strategy synthesis on automata encoding motion of agents in spaces represented by images, as well as a proof-of-concept realistic example based on a case study from the railway domain. The strategies are synthesised with , while the properties to enforce are defined by means of spatial model checking of the images with . The combination of spatial model checking with strategy synthesis provides a toolchain for checking and enforcing mobility properties in multi-agent systems in which location plays an important role, like in many collective adaptive systems. We discuss the toolchain’s performance also considering several recent improvements.

Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed for the topological interpretation of Modal Logic. The Spatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachability connectives that, in turn, can be used for expressing interesting spatial properties, such as "being near to" or "being surrounded by". SLCS constitutes the kernel of a solid logical framework for reasoning about discrete space, such as graphs and digital images, interpreted as quasi discrete closure spaces. Following a recently developed geometric semantics of Modal Logic, we propose an interpretation of SLCS in continuous space, admitting a geometric spatial model checking procedure, by resorting to models based on polyhedra. Such representations of space are increasingly relevant in many domains of application, due to recent developments of 3D scanning and visualisation techniques that exploit mesh processing. We introduce PolyLogicA, a geometric spatial model checker for SLCS formulas on polyhedra and demonstrate feasibility of our approach on two 3D polyhedral models of realistic size. Finally, we introduce a geometric definition of bisimilarity, proving that it characterises logical equivalence.

In this work, we provide a simple coalgebraic characterisation of regular omega-languages based on languages of lassos, and prove a number of related mathematical results, framed into the theory of a new kind of automata called Omega-automata. In earlier work we introduced Omega-automata as two-sorted structures that naturally operate on lassos, pairs of words encoding ultimately periodic streams (infinite words). Here we extend the scope of these Omega-automata by proposing them as a new kind of acceptor for arbitrary streams. We prove that Omega-automata are expressively complete for the regular omega-languages. We show that, due to their coalgebraic nature, Omega-automata share some attractive properties with deterministic automata operating on finite words, properties that other types of stream automata lack. In particular, we provide a simple, coalgebraic definition of bisimilarity between Omega-automata that exactly captures language equivalence and allows for a simple minimization procedure. We also prove a coalgebraic Myhill-Nerode style theorem for lasso languages, and use this result, in combination with a closure property on stream languages called lasso determinacy, to give a characterization of regular omega-languages.

Spatial and spatio-temporal model checking techniques have a wide range of application domains, among which large scale distributed systems and signal and image analysis. We explore a new domain, namely (semi-)automatic contouring in Medical Imaging, introducing the tool VoxLogicA which merges the state-of-the-art library of computational imaging algorithms ITK with the unique combination of declarative specification and optimised execution provided by spatial logic model checking. The result is a rapid , logic based analysis development methodology. The analysis of an existing benchmark of medical images for segmentation of brain tumours shows that simple VoxLogicA analysis can reach state-of-the-art accuracy, competing with best-in-class algorithms, with the advantage of explainability and easy replicability . Furthermore, due to a two-orders-of-magnitude speedup compared to the existing general-purpose spatio-temporal model checker topochecker , VoxLogicA enables interactive development of analysis of 3D medical images, which can greatly facilitate the work of professionals in this domain.

We present an experience in modelling and statistical model checking a satellite-based moving block signalling scenario from the railway industry with Uppaal SMC. This demonstrates the usability and applicability of Uppaal SMC in the railway domain. We also propose a promising direction for future work, in which we envision spatio-temporal analysis with Uppaal SMC.

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

We describe a formal methodology for the automatic synthesis of a secure orchestrator for a set of BPMN processes. The synthesized orchestrator is able to guarantee that all the processes that are started reach their end, and the resulting orchestrator process is secure, that is, it does not allow discloure of certain secret messages. In this work we present an implementation of a forth and back translation from BPMN to crypto-CCS, in such a way to exploit the PaMoChSA tool for synthesizing orchestrators. Furthermore, we study the problem of ranking orchestrators based on quantitative valuations of a process, and on the temporal evolution of such valuations and their security, as a function of the knowledge of the attacker.