90 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
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
On Bisimilarity for Quasi-discrete Closure Spaces
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.
CM-bisimilarity corresponds to equivalence with respect to the infinitary modal
logic IML that includes the modality for ``being near''. (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 and Converse , stemming from
the binary relation underlying closure and its converse. CMC-bisimilarity, is
captured by the infinitary modal logic IMLC including two modalities, Direct
and Converse , 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 and Converse , 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 structures.Comment: 32 pages, 14 figure
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