673,395 research outputs found
Model-Checking Process Equivalences
Process equivalences are formal methods that relate programs and system
which, informally, behave in the same way. Since there is no unique notion of
what it means for two dynamic systems to display the same behaviour there are a
multitude of formal process equivalences, ranging from bisimulation to trace
equivalence, categorised in the linear-time branching-time spectrum.
We present a logical framework based on an expressive modal fixpoint logic
which is capable of defining many process equivalence relations: for each such
equivalence there is a fixed formula which is satisfied by a pair of processes
if and only if they are equivalent with respect to this relation. We explain
how to do model checking, even symbolically, for a significant fragment of this
logic that captures many process equivalences. This allows model checking
technology to be used for process equivalence checking. We show how partial
evaluation can be used to obtain decision procedures for process equivalences
from the generic model checking scheme.Comment: In Proceedings GandALF 2012, arXiv:1210.202
Lumpy Structures in Self-Gravitating Disks
Following Toomre & Kalnajs (1991), local models of slightly dissipative
self-gravitating disks show how inhomogeneous structures can be maintained over
several galaxy rotations. Their basic physical ingredients are self-gravity,
dissipation and differential rotation. In order to explore the structures
resulting from these processes on the kpc scale, local simulation of
self-gravitating disks are performed in this paper in 2D as well as in 3D. The
third dimension becomes a priori important as soon as matter clumping causes a
tight coupling of the 3D equations of motion. The physically simple and general
framework of the model permits to make conclusions beyond the here considered
scales. A time dependent affine coordinate system is used, allowing to
calculate the gravitational forces via a particle-mesh FFT-method, increasing
the performance with respect to previous direct force calculations. Persistent
patterns, formed by transient structures, whose intensity and morphological
characteristic depend on the dissipation rate are obtained and described. Some
of our simulations reveal first signs of mass-size and velocity dispersion-size
power-law relations, but a clear scale invariant behavior will require more
powerful computer techniques.Comment: 28 pages, 32 figures. Accepted for publication in A&A. Full
resolution paper available at http://obswww.unige.ch/Preprints/dyn_art.htm
A theory of normed simulations
In existing simulation proof techniques, a single step in a lower-level
specification may be simulated by an extended execution fragment in a
higher-level one. As a result, it is cumbersome to mechanize these techniques
using general purpose theorem provers. Moreover, it is undecidable whether a
given relation is a simulation, even if tautology checking is decidable for the
underlying specification logic. This paper introduces various types of normed
simulations. In a normed simulation, each step in a lower-level specification
can be simulated by at most one step in the higher-level one, for any related
pair of states. In earlier work we demonstrated that normed simulations are
quite useful as a vehicle for the formalization of refinement proofs via
theorem provers. Here we show that normed simulations also have pleasant
theoretical properties: (1) under some reasonable assumptions, it is decidable
whether a given relation is a normed forward simulation, provided tautology
checking is decidable for the underlying logic; (2) at the semantic level,
normed forward and backward simulations together form a complete proof method
for establishing behavior inclusion, provided that the higher-level
specification has finite invisible nondeterminism.Comment: 31 pages, 10figure
Intrinsic Simulations between Stochastic Cellular Automata
The paper proposes a simple formalism for dealing with deterministic,
non-deterministic and stochastic cellular automata in a unifying and composable
manner. Armed with this formalism, we extend the notion of intrinsic simulation
between deterministic cellular automata, to the non-deterministic and
stochastic settings. We then provide explicit tools to prove or disprove the
existence of such a simulation between two stochastic cellular automata, even
though the intrinsic simulation relation is shown to be undecidable in
dimension two and higher. The key result behind this is the caracterization of
equality of stochastic global maps by the existence of a coupling between the
random sources. We then prove that there is a universal non-deterministic
cellular automaton, but no universal stochastic cellular automaton. Yet we
provide stochastic cellular automata achieving optimal partial universality.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
Numerical simulations of the Fourier transformed Vlasov-Maxwell system in higher dimensions --- Theory and applications
We present a review of recent developments of simulations of the
Vlasov-Maxwell system of equations using a Fourier transform method in velocity
space. In this method, the distribution functions for electrons and ions are
Fourier transformed in velocity space, and the resulting set of equations are
solved numerically. In the original Vlasov equation, phase mixing may lead to
an oscillatory behavior and sharp gradients of the distribution function in
velocity space, which is problematic in simulations where it can lead to
unphysical electric fields and instabilities and to the recurrence effect where
parts of the initial condition recur in the simulation. The particle
distribution function is in general smoother in the Fourier transformed
velocity space, which is desirable for the numerical approximations. By
designing outflow boundary conditions in the Fourier transformed velocity
space, the highest oscillating terms are allowed to propagate out through the
boundary and are removed from the calculations, thereby strongly reducing the
numerical recurrence effect. The outflow boundary conditions in higher
dimensions including electromagnetic effects are discussed. The Fourier
transform method is also suitable to solve the Fourier transformed Wigner
equation, which is the quantum mechanical analogue of the Vlasov equation for
classical particles.Comment: 41 pages, 19 figures. To be published in Transport Theory and
Statistical Physics. Proceedings of the VLASOVIA 2009 Workshop, CIRM, Luminy,
Marseilles, France, 31 August - 4 September 200
Numerical and Theoretical Study of a Monodisperse Hard-Sphere Glass Former
There exists a variety of theories of the glass transition and many more
numerical models. But because the models need built-in complexity to prevent
crystallization, comparisons with theory can be difficult. We study the
dynamics of a deeply supersaturated \emph{monodisperse} four-dimensional (4D)
hard-sphere fluid, which has no such complexity, but whose strong intrinsic
geometrical frustration inhibits crystallization, even when deeply
supersaturated. As an application, we compare its behavior to the mode-coupling
theory (MCT) of glass formation. We find MCT to describe this system better
than any other structural glass formers in lower dimensions. The reduction in
dynamical heterogeneity in 4D suggested by a milder violation of the
Stokes-Einstein relation could explain the agreement. These results are
consistent with a mean-field scenario of the glass transition.Comment: 5 pages, 3 figure
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