1,617 research outputs found
Stabilizing Maximal Independent Set in Unidirectional Networks is Hard
A distributed algorithm is self-stabilizing if after faults and attacks hit
the system and place it in some arbitrary global state, the system recovers
from this catastrophic situation without external intervention in finite time.
In this paper, we consider the problem of constructing self-stabilizingly a
\emph{maximal independent set} in uniform unidirectional networks of arbitrary
shape. On the negative side, we present evidence that in uniform networks,
\emph{deterministic} self-stabilization of this problem is \emph{impossible}.
Also, the \emph{silence} property (\emph{i.e.} having communication fixed from
some point in every execution) is impossible to guarantee, either for
deterministic or for probabilistic variants of protocols. On the positive side,
we present a deterministic protocol for networks with arbitrary unidirectional
networks with unique identifiers that exhibits polynomial space and time
complexity in asynchronous scheduling. We complement the study with
probabilistic protocols for the uniform case: the first probabilistic protocol
requires infinite memory but copes with asynchronous scheduling, while the
second probabilistic protocol has polynomial space complexity but can only
handle synchronous scheduling. Both probabilistic solutions have expected
polynomial time complexity
Self-Stabilization in the Distributed Systems of Finite State Machines
The notion of self-stabilization was first proposed by Dijkstra in 1974 in his classic paper. The paper defines a system as self-stabilizing if, starting at any, possibly illegitimate, state the system can automatically adjust itself to eventually converge to a legitimate state in finite amount of time and once in a legitimate state it will remain so unless it incurs a subsequent transient fault. Dijkstra limited his attention to a ring of finite-state machines and provided its solution for self-stabilization. In the years following his introduction, very few papers were published in this area. Once his proposal was recognized as a milestone in work on fault tolerance, the notion propagated among the researchers rapidly and many researchers in the distributed systems diverted their attention to it. The investigation and use of self-stabilization as an approach to fault-tolerant behavior under a model of transient failures for distributed systems is now undergoing a renaissance. A good number of works pertaining to self-stabilization in the distributed systems were proposed in the yesteryears most of which are very recent. This report surveys all previous works available in the literature of self-stabilizing systems
Local algorithms : Self-stabilization on speed
Non peer reviewe
On the Limits and Practice of Automatically Designing Self-Stabilization
A protocol is said to be self-stabilizing when the distributed system executing it is guaranteed to recover from any fault that does not cause permanent damage. Designing such protocols is hard since they must recover from all possible states, therefore we investigate how feasible it is to synthesize them automatically. We show that synthesizing stabilization on a fixed topology is NP-complete in the number of system states. When a solution is found, we further show that verifying its correctness on a general topology (with any number of processes) is undecidable, even for very simple unidirectional rings. Despite these negative results, we develop an algorithm to synthesize a self-stabilizing protocol given its desired topology, legitimate states, and behavior. By analogy to shadow puppetry, where a puppeteer may design a complex puppet to cast a desired shadow, a protocol may need to be designed in a complex way that does not even resemble its specification. Our shadow/puppet synthesis algorithm addresses this concern and, using a complete backtracking search, has automatically designed 4 new self-stabilizing protocols with minimal process space requirements: 2-state maximal matching on bidirectional rings, 5-state token passing on unidirectional rings, 3-state token passing on bidirectional chains, and 4-state orientation on daisy chains
Biological evolution through mutation, selection, and drift: An introductory review
Motivated by present activities in (statistical) physics directed towards
biological evolution, we review the interplay of three evolutionary forces:
mutation, selection, and genetic drift. The review addresses itself to
physicists and intends to bridge the gap between the biological and the
physical literature. We first clarify the terminology and recapitulate the
basic models of population genetics, which describe the evolution of the
composition of a population under the joint action of the various evolutionary
forces. Building on these foundations, we specify the ingredients explicitly,
namely, the various mutation models and fitness landscapes. We then review
recent developments concerning models of mutational degradation. These predict
upper limits for the mutation rate above which mutation can no longer be
controlled by selection, the most important phenomena being error thresholds,
Muller's ratchet, and mutational meltdowns. Error thresholds are deterministic
phenomena, whereas Muller's ratchet requires the stochastic component brought
about by finite population size. Mutational meltdowns additionally rely on an
explicit model of population dynamics, and describe the extinction of
populations. Special emphasis is put on the mutual relationship between these
phenomena. Finally, a few connections with the process of molecular evolution
are established.Comment: 62 pages, 6 figures, many reference
Polynomial-Time Space-Optimal Silent Self-Stabilizing Minimum-Degree Spanning Tree Construction
Motivated by applications to sensor networks, as well as to many other areas,
this paper studies the construction of minimum-degree spanning trees. We
consider the classical node-register state model, with a weakly fair scheduler,
and we present a space-optimal \emph{silent} self-stabilizing construction of
minimum-degree spanning trees in this model. Computing a spanning tree with
minimum degree is NP-hard. Therefore, we actually focus on constructing a
spanning tree whose degree is within one from the optimal. Our algorithm uses
registers on bits, converges in a polynomial number of rounds, and
performs polynomial-time computation at each node. Specifically, the algorithm
constructs and stabilizes on a special class of spanning trees, with degree at
most . Indeed, we prove that, unless NP coNP, there are no
proof-labeling schemes involving polynomial-time computation at each node for
the whole family of spanning trees with degree at most . Up to our
knowledge, this is the first example of the design of a compact silent
self-stabilizing algorithm constructing, and stabilizing on a subset of optimal
solutions to a natural problem for which there are no time-efficient
proof-labeling schemes. On our way to design our algorithm, we establish a set
of independent results that may have interest on their own. In particular, we
describe a new space-optimal silent self-stabilizing spanning tree
construction, stabilizing on \emph{any} spanning tree, in rounds, and
using just \emph{one} additional bit compared to the size of the labels used to
certify trees. We also design a silent loop-free self-stabilizing algorithm for
transforming a tree into another tree. Last but not least, we provide a silent
self-stabilizing algorithm for computing and certifying the labels of a
NCA-labeling scheme
Noise enhanced coupling between two oscillators with long-term plasticity
Spike time-dependent plasticity is a fundamental adaptation mechanism of the nervous system. It induces structural changes of synaptic connectivity by regulation of coupling strengths between individual cells depending on their spiking behavior. As a biophysical process its functioning is constantly subjected to natural fluctuations. We study theoretically the influence of noise on a microscopic level by considering only two coupled neurons. Adopting a phase description for the neurons we derive a two-dimensional system which describes the averaged dynamics of the coupling strengths. We show that a multistability of several coupling configurations is possible, where some configurations are not found in systems without noise. Intriguingly, it is possible that a strong bidirectional coupling, which is not present in the noise-free situation, can be stabilized by the noise. This means that increased noise, which is normally expected to desynchronize the neurons, can be the reason for an antagonistic response of the system, which organizes itself into a state of stronger coupling and counteracts the impact of noise. This mechanism, as well as a high potential for multistability, is also demonstrated numerically for a coupled pair of Hodgkin-Huxley neurons
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