216,964 research outputs found
Exact Solution of a Jamming Transition: Closed Equations for a Bootstrap Percolation Problem
Jamming, or dynamical arrest, is a transition at which many particles stop
moving in a collective manner. In nature it is brought about by, for example,
increasing the packing density, changing the interactions between particles, or
otherwise restricting the local motion of the elements of the system. The onset
of collectivity occurs because, when one particle is blocked, it may lead to
the blocking of a neighbor. That particle may then block one of its neighbors,
these effects propagating across some typical domain of size named the
dynamical correlation length. When this length diverges, the system becomes
immobile. Even where it is finite but large the dynamics is dramatically
slowed. Such phenomena lead to glasses, gels, and other very long-lived
nonequilibrium solids. The bootstrap percolation models are the simplest
examples describing these spatio-temporal correlations. We have been able to
solve one such model in two dimensions exactly, exhibiting the precise
evolution of the jamming correlations on approach to arrest. We believe that
the nature of these correlations and the method we devise to solve the problem
are quite general. Both should be of considerable help in further developing
this field.Comment: 17 pages, 4 figure
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
A guided tour of asynchronous cellular automata
Research on asynchronous cellular automata has received a great amount of
attention these last years and has turned to a thriving field. We survey the
recent research that has been carried out on this topic and present a wide
state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
Benchmarks for Parity Games (extended version)
We propose a benchmark suite for parity games that includes all benchmarks
that have been used in the literature, and make it available online. We give an
overview of the parity games, including a description of how they have been
generated. We also describe structural properties of parity games, and using
these properties we show that our benchmarks are representative. With this work
we provide a starting point for further experimentation with parity games.Comment: The corresponding tool and benchmarks are available from
https://github.com/jkeiren/paritygame-generator. This is an extended version
of the paper that has been accepted for FSEN 201
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