31 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
Coinduction up to in a fibrational setting
Bisimulation up-to enhances the coinductive proof method for bisimilarity,
providing efficient proof techniques for checking properties of different kinds
of systems. We prove the soundness of such techniques in a fibrational setting,
building on the seminal work of Hermida and Jacobs. This allows us to
systematically obtain up-to techniques not only for bisimilarity but for a
large class of coinductive predicates modelled as coalgebras. By tuning the
parameters of our framework, we obtain novel techniques for unary predicates
and nominal automata, a variant of the GSOS rule format for similarity, and a
new categorical treatment of weak bisimilarity
Nominal Cellular Automata
In Proceedings ICE 2016, arXiv:1608.0313
Automata theory in nominal sets
We study languages over infinite alphabets equipped with some structure that
can be tested by recognizing automata. We develop a framework for studying such
alphabets and the ensuing automata theory, where the key role is played by an
automorphism group of the alphabet. In the process, we generalize nominal sets
due to Gabbay and Pitts
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