23,816 research outputs found
Domain Representable Spaces Defined by Strictly Positive Induction
Recursive domain equations have natural solutions. In particular there are
domains defined by strictly positive induction. The class of countably based
domains gives a computability theory for possibly non-countably based
topological spaces. A space is a topological space characterized by
its strong representability over domains. In this paper, we study strictly
positive inductive definitions for spaces by means of domain
representations, i.e. we show that there exists a canonical fixed point of
every strictly positive operation on spaces.Comment: 48 pages. Accepted for publication in Logical Methods in Computer
Scienc
A knowledge-based system with learning for computer communication network design
Computer communication network design is well-known as complex and hard. For that reason, the most effective methods used to solve it are heuristic. Weaknesses of these techniques are listed and a new approach based on artificial intelligence for solving this problem is presented. This approach is particularly recommended for large packet switched communication networks, in the sense that it permits a high degree of reliability and offers a very flexible environment dealing with many relevant design parameters such as link cost, link capacity, and message delay
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
A Bochner Type Theorem for Inductive Limits of Gelfand Pairs
In this paper we prove a generalisation of Bochner's theorem. Our result
deals with Olshanski's spherical pairs defined as inductive limits of
increasing sequences of Gelfand Pairs.Comment: 17 pages, To appear in Annales de l'Institut Fourier, Volume 58, 200
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
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