449,744 research outputs found
Termination Detection of Local Computations
Contrary to the sequential world, the processes involved in a distributed
system do not necessarily know when a computation is globally finished. This
paper investigates the problem of the detection of the termination of local
computations. We define four types of termination detection: no detection,
detection of the local termination, detection by a distributed observer,
detection of the global termination. We give a complete characterisation
(except in the local termination detection case where a partial one is given)
for each of this termination detection and show that they define a strict
hierarchy. These results emphasise the difference between computability of a
distributed task and termination detection. Furthermore, these
characterisations encompass all standard criteria that are usually formulated :
topological restriction (tree, rings, or triangu- lated networks ...),
topological knowledge (size, diameter ...), and local knowledge to distinguish
nodes (identities, sense of direction). These results are now presented as
corollaries of generalising theorems. As a very special and important case, the
techniques are also applied to the election problem. Though given in the model
of local computations, these results can give qualitative insight for similar
results in other standard models. The necessary conditions involve graphs
covering and quasi-covering; the sufficient conditions (constructive local
computations) are based upon an enumeration algorithm of Mazurkiewicz and a
stable properties detection algorithm of Szymanski, Shi and Prywes
Dynamic Dependency Pairs for Algebraic Functional Systems
We extend the higher-order termination method of dynamic dependency pairs to
Algebraic Functional Systems (AFSs). In this setting, simply typed lambda-terms
with algebraic reduction and separate {\beta}-steps are considered. For
left-linear AFSs, the method is shown to be complete. For so-called local AFSs
we define a variation of usable rules and an extension of argument filterings.
All these techniques have been implemented in the higher-order termination tool
WANDA
Speeding up active mesh segmentation by local termination of nodes.
This article outlines a procedure for speeding up segmentation of images using active mesh systems. Active meshes and other deformable models are very popular in image segmentation due to their ability to capture weak or missing boundary information; however, where strong edges exist, computations are still done after mesh nodes have settled on the boundary. This can lead to extra computational time whilst the system continues to deform completed regions of the mesh. We propose a local termination procedure, reducing these unnecessary computations and speeding up segmentation time with minimal loss of quality
Local Termination: theory and practice
The characterisation of termination using well-founded monotone algebras has
been a milestone on the way to automated termination techniques, of which we
have seen an extensive development over the past years. Both the semantic
characterisation and most known termination methods are concerned with global
termination, uniformly of all the terms of a term rewriting system (TRS). In
this paper we consider local termination, of specific sets of terms within a
given TRS. The principal goal of this paper is generalising the semantic
characterisation of global termination to local termination. This is made
possible by admitting the well-founded monotone algebras to be partial. We also
extend our approach to local relative termination. The interest in local
termination naturally arises in program verification, where one is probably
interested only in sensible inputs, or just wants to characterise the set of
inputs for which a program terminates. Local termination will be also be of
interest when dealing with a specific class of terms within a TRS that is known
to be non-terminating, such as combinatory logic (CL) or a TRS encoding
recursive program schemes or Turing machines. We show how some of the
well-known techniques for proving global termination, such as stepwise removal
of rewrite rules and semantic labelling, can be adapted to the local case. We
also describe transformations reducing local to global termination problems.
The resulting techniques for proving local termination have in some cases
already been automated. One of our applications concerns the characterisation
of the terminating S-terms in CL as regular language. Previously this language
had already been found via a tedious analysis of the reduction behaviour of
S-terms. These findings have now been vindicated by a fully automated and
verified proof
Non-simplifying Graph Rewriting Termination
So far, a very large amount of work in Natural Language Processing (NLP) rely
on trees as the core mathematical structure to represent linguistic
informations (e.g. in Chomsky's work). However, some linguistic phenomena do
not cope properly with trees. In a former paper, we showed the benefit of
encoding linguistic structures by graphs and of using graph rewriting rules to
compute on those structures. Justified by some linguistic considerations, graph
rewriting is characterized by two features: first, there is no node creation
along computations and second, there are non-local edge modifications. Under
these hypotheses, we show that uniform termination is undecidable and that
non-uniform termination is decidable. We describe two termination techniques
based on weights and we give complexity bound on the derivation length for
these rewriting system.Comment: In Proceedings TERMGRAPH 2013, arXiv:1302.599
Ribosome recycling, diffusion, and mRNA loop formation in translational regulation
We explore and quantify the physical and biochemical mechanisms that may be
relevant in the regulation of translation. After elongation and detachment from
the 3' termination site of mRNA, parts of the ribosome machinery can diffuse
back to the initiation site, especially if it is held nearby, enhancing overall
translation rates. The elongation steps of the mRNA-bound ribosomes are modeled
using exact and asymptotic results of the totally asymmetric exclusion process
(TASEP).Since the ribosome injection rates of the TASEP depend on the local
concentrations at the initiation site, a source of ribosomes emanating from the
termination end can feed back to the initiation site, leading to a
self-consistent set of equations for the steady-state ribosome throughput.
Additional mRNA binding factors can also promote loop formation, or
cyclization, bringing the initiation and termination sites into close
proximity. The probability distribution of the distance between the initiation
and termination sites is described using simple noninteracting polymer models.
We find that the initiation, or initial ribosome adsorption binding required
for maximal throughput can vary dramatically depending on certain values of the
bulk ribosome concentration and diffusion constant. If cooperative interactions
among the loop-promoting proteins and the initiation/termination sites are
considered, the throughput can be further regulated in a nonmonotonic manner.
Potential experiments to test the hypothesized physical mechanisms are
discussed.Comment: 21 pp, 11 .eps figs, realigned figures and magin
Termination of rewriting strategies: a generic approach
We propose a generic termination proof method for rewriting under strategies,
based on an explicit induction on the termination property. Rewriting trees on
ground terms are modeled by proof trees, generated by alternatively applying
narrowing and abstracting steps. The induction principle is applied through the
abstraction mechanism, where terms are replaced by variables representing any
of their normal forms. The induction ordering is not given a priori, but
defined with ordering constraints, incrementally set during the proof.
Abstraction constraints can be used to control the narrowing mechanism, well
known to easily diverge. The generic method is then instantiated for the
innermost, outermost and local strategies.Comment: 49 page
Calculation of skin-stiffener interface stresses in stiffened composite panels
A method for computing the skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The finite-element analysis is standard, while the elasticity solution is based on an eigenvalue expansion of the stress functions. The eigenvalue expansion is assumed to be valid in the local flange termination region and is coupled with the finite-element analysis using collocation of stresses on the local region boundaries. Accuracy and convergence of the local elasticity solution are assessed using a geometrically linear analysis. Using this analysis procedure, the influence of geometric nonlinearities and stiffener parameters on the skin-stiffener interface stresses is evaluated
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