Model Checking Spatial Logics for Closure Spaces

Spatial aspects of computation are becoming increasingly relevant in Computer Science, especially in the field of collective adaptive systems and when dealing with systems distributed in physical space. Traditional formal verification techniques are well suited to analyse the temporal evolution of programs; however, properties of space are typically not taken into account explicitly. We present a topology-based approach to formal verification of spatial properties depending upon physical space. We define an appropriate logic, stemming from the tradition of topological interpretations of modal logics, dating back to earlier logicians such as Tarski, where modalities describe neighbourhood. We lift the topological definitions to the more general setting of closure spaces, also encompassing discrete, graph-based structures. We extend the framework with a spatial surrounded operator, a propagation operator and with some collective operators. The latter are interpreted over arbitrary sets of points instead of individual points in space. We define efficient model checking procedures, both for the individual and the collective spatial fragments of the logic and provide a proof-of-concept tool

Specifying and Verifying Properties of Space - Extended Version

The interplay between process behaviour and spatial aspects of computation has become more and more relevant in Computer Science, especially in the field of collective adaptive systems, but also, more generally, when dealing with systems distributed in physical space. Traditional verification techniques are well suited to analyse the temporal evolution of programs; properties of space are typically not explicitly taken into account. We propose a methodology to verify properties depending upon physical space. We define an appropriate logic, stemming from the tradition of topological interpretations of modal logics, dating back to earlier logicians such as Tarski, where modalities describe neighbourhood. We lift the topological definitions to a more general setting, also encompassing discrete, graph-based structures. We further extend the framework with a spatial until operator, and define an efficient model checking procedure, implemented in a proof-of-concept tool.Comment: Presented at "Theoretical Computer Science" 2014, Rom

Nominal Cellular Automata

In Proceedings ICE 2016, arXiv:1608.0313

A temporal logic for HD-automata

Due to the broad diffusion of every kind of network and mobile device in the last few years, computing is rapidly evolving towards what is now called "global computing". With this term we refer to a new field of research and development in computer science, with innovative features with respects to standard development processes and software architectures: computing is distributed and mobile, programs are heterogeneous, systems are open-ended, computational entities are autonomous. To completely meet these goals in software production, work is required from the theoretical point of view, both to develop new models of computation that satisfy the given requirements, and to learn how to reason about the behavior, and check properties, of such systems. In this thesis, we will concentrate on a particular operational model called history dependent automata, an enriched version of labeled transition systems that can represent name generation and name passing, and is particularly adapt to model in a compact way finite state, concurrent mobile systems. We develop a temporal logic for pi calculus and HD-automata, provide proofs of adequacy, soundness and completeness, and describe the model checking algorithm. Case studies are provided which reveal the expressive power of the logic

Families of Symmetries as Efficient Models of Resource Binding

AbstractCalculi that feature resource-allocating constructs (e.g. the pi-calculus or the fusion calculus) require special kinds of models. The best-known ones are presheaves and nominal sets. But named sets have the advantage of being finite in a wide range of cases where the other two are infinite. The three models are equivalent. Finiteness of named sets is strictly related to the notion of finite support in nominal sets and the corresponding presheaves. We show that named sets are generalisd by the categorical model of families, that is, free coproduct completions, indexed by symmetries, and explain how locality of interfaces gives good computational properties to families. We generalise previous equivalence results by introducing a notion of minimal support in presheaf categories indexed over small categories of monos. Functors and categories of coalgebras may be defined over families. We show that the final coalgebra has the greatest possible symmetry up-to bisimilarity, which can be computed by iteration along the terminal sequence, thanks to finiteness of the representation

Geometric Model Checking of Continuous Space

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