Vincenzo Ciancia

Specifying and Verifying Properties of Space

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.

Spatial Logic and Spatial Model Checking for Closure Spaces

Spatial aspects of computation are 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 concurrent systems; however, properties of space are typically not explicitly taken into account. This tutorial provides an introduction to recent work on a topology-inspired approach to formal verification of spatial properties depending upon physical space. A logic is presented, stemming from the tradition of topological interpretations of modal logics, dating back to earlier logicians such as Tarski, where modalities describe neighbourhood. These topological definitions are lifted to the more general setting of closure spaces, also encompassing discrete, graph-based structures. The present tutorial illustrates the extension of the framework with a spatial surrounded operator, leading to the spatial logic for closure spaces SLCS, and its combination with the temporal logic CTL, leading to STLCS. The interplay of space and time permits one to define complex spatio-temporal properties. Both for the spatial and the spatio-temporal fragment efficient model-checking algorithms have been developed and their use on a number of case studies and examples is illustrated.

An Experimental Spatio-Temporal Model Checker

In this work we present a spatial extension of the global model checking algorithm of the temporal logic CTL. This classical verification framework is augmented with ideas coming from the tradition of topological spatial logics. More precisely, we add to CTL the operators of the Spatial Logic of Closure Spaces, including the surrounded operator, with its intended meaning of a point being surrounded by entities satisfying a specific property. The interplay of space and time permits one to define complex spatio-temporal properties. The model checking algorithm that we propose features no particular efficiency optimisations, as it is meant to be a reference specification of a family of more efficient algorithms that are planned for future work. Its complexity depends on the product of temporal states and points of the space. Nevertheless, a prototype model checker has been implemented, made available, and used for experimentation of the application of spatio-temporal verification in the field of collective adaptive systems.

A Tool-Chain for Statistical Spatio-Temporal Model Checking of Bike Sharing Systems

Prominent examples of collective systems are often encountered when analysing smart cities and smart transportation systems. We propose a novel modelling and analysis approach combining statistical model checking, spatio-temporal logics, and simulation. The proposed methodology is applied to modelling and statistical analysis of user behaviour in bike sharing systems. We present a tool-chain that integrates the statistical analysis toolkit MultiVeStA, the spatio-temporal model checker topochecker, and a bike sharing systems simulator based on Markov renewal processes. The obtained tool allows one to estimate, up to a user-specified precision, the likelihood of specific spatio-temporal formulas, such as the formation of clusters of full stations and their temporal evolution.

From Collective Adaptive Systems to Human Centric Computation and Back: Spatial Model Checking for Medical Imaging.

Recent research on formal verification for Collective Adaptive Systems (CAS) pushed advancements in spatial and spatio-temporal model checking, and as a side result provided novel image analysis methodologies, rooted in logical methods for topological spaces. Medical Imaging (MI) is a field where such technologies show potential for ground-breaking innovation. In this position paper, we present a preliminary investigation centred on applications of spatial model checking to MI. The focus is shifted from pure logics to a mixture of logical, statistical and algorithmic approaches, driven by the logical nature intrinsic to the specification of the properties of interest in the field. As a result, novel operators are introduced, that could as well be brought back to the setting of CAS.

Nominal Cellular Automata.

The emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their computational capabilities, with a special focus on the emergent behavioural properties of this new model and their significance in the context of computation-oriented interpretations of physical phenomena. A preliminary investigation of the relations between Nominal Cellular Automata and Wolframs Elementary Cellular Automata is also carried out.

From urelements to Computation

Around 1922-1938, a new permutation model of set theory was defined. The permutation model served as a counterexample in the first proof of independence of the Axiom of Choice from the other axioms of Zermelo-Fraenkel set theory. Almost a century later, a model introduced as part of a proof in abstract mathematics fostered a plethora of research results, ranging from the area of syntax and semantics of programming languages to minimization algorithms and automated verification of systems. Among these results, we find Lawvere-style algebraic syntax with binders, final-coalgebra semantics with resource allocation, and minimization algorithms for mobile systems. These results are also obtained in various different ways, by describing, in terms of category theory, a number of models equivalent to the permutation model.

A Class of Automata for the Verification of Infinite, Resource-Allocating Behaviours

Process calculi for service-oriented computing often feature generation of fresh resources. So-called nominal automata have been studied both as semantic models for such calculi, and as acceptors of languages of finite words over infinite alphabets. In this paper we investigate nominal automata that accept infinite words. These automata are a generalisation of deterministic Muller automata to the setting of nominal sets. We prove decidability of complement, union, intersection, emptiness and equivalence, and determinacy by ultimately periodic words. The key to obtain such results is to use finite representations of the (otherwise infinite-state) defined class of automata. The definition of such operations enables model checking of process calculi featuring infinite behaviours, and resource allocation, to be implemented using classical automata-theoretic methods.

Exploring nominal cellular automata

The emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their computational capabilities, with a special focus on the emergent behavioural properties of this new model and their significance in the context of computation-oriented interpretations of physical phenomena. An investigation of the relations between Nominal Cellular Automata and Wolframs Elementary Cellular Automata is carried out, together with an analysis of interesting particles, exhibiting “nominal” behaviour, in a particular kind of rules, reminiscent of the class of totalistic Cellular Automata, that we call “bagged”.

Interaction and Observation: Categorical Semantics of Reactive Systems Trough Dialgebras

We use dialgebras, generalising both algebras and coalgebras, as a complement of the standard coalgebraic framework, aimed at describing the semantics of an interactive system by the means of reaction rules. In this model, interaction is built-in, and semantic equivalence arises from it, instead of being determined by a (possibly difficult) understanding of the side effects of a component in isolation. Behavioural equivalence in dialgebras is determined by how a given process interacts with the others, and the obtained observations. We develop a technique to inter-define categories of dialgebras of different functors, that in particular permits us to compare a standard coalgebraic semantics and its dialgebraic counterpart. We exemplify the framework using the CCS and the pi-calculus. Remarkably, the dialgebra giving semantics to the pi-calculus does not require the use of presheaf categories.