2,300 research outputs found
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
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
On Formal Methods for Collective Adaptive System Engineering. {Scalable Approximated, Spatial} Analysis Techniques. Extended Abstract
In this extended abstract a view on the role of Formal Methods in System
Engineering is briefly presented. Then two examples of useful analysis
techniques based on solid mathematical theories are discussed as well as the
software tools which have been built for supporting such techniques. The first
technique is Scalable Approximated Population DTMC Model-checking. The second
one is Spatial Model-checking for Closure Spaces. Both techniques have been
developed in the context of the EU funded project QUANTICOL.Comment: In Proceedings FORECAST 2016, arXiv:1607.0200
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
VoxLogicA : A Spatial Model Checker for Declarative Image Analysis
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 generalpurpose 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
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
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