10,093 research outputs found
Weak vs. Self vs. Probabilistic Stabilization
Self-stabilization is a strong property that guarantees that a network always
resume correct behavior starting from an arbitrary initial state. Weaker
guarantees have later been introduced to cope with impossibility results:
probabilistic stabilization only gives probabilistic convergence to a correct
behavior. Also, weak stabilization only gives the possibility of convergence.
In this paper, we investigate the relative power of weak, self, and
probabilistic stabilization, with respect to the set of problems that can be
solved. We formally prove that in that sense, weak stabilization is strictly
stronger that self-stabilization. Also, we refine previous results on weak
stabilization to prove that, for practical schedule instances, a deterministic
weak-stabilizing protocol can be turned into a probabilistic self-stabilizing
one. This latter result hints at more practical use of weak-stabilization, as
such algorthms are easier to design and prove than their (probabilistic)
self-stabilizing counterparts
Dynamic FTSS in Asynchronous Systems: the Case of Unison
Distributed fault-tolerance can mask the effect of a limited number of
permanent faults, while self-stabilization provides forward recovery after an
arbitrary number of transient fault hit the system. FTSS protocols combine the
best of both worlds since they are simultaneously fault-tolerant and
self-stabilizing. To date, FTSS solutions either consider static (i.e. fixed
point) tasks, or assume synchronous scheduling of the system components. In
this paper, we present the first study of dynamic tasks in asynchronous
systems, considering the unison problem as a benchmark. Unison can be seen as a
local clock synchronization problem as neighbors must maintain digital clocks
at most one time unit away from each other, and increment their own clock value
infinitely often. We present many impossibility results for this difficult
problem and propose a FTSS solution when the problem is solvable that exhibits
optimal fault containment
Scatter of Weak Robots
In this paper, we first formalize the problem to be solved, i.e., the Scatter
Problem (SP). We then show that SP cannot be deterministically solved. Next, we
propose a randomized algorithm for this problem. The proposed solution is
trivially self-stabilizing. We then show how to design a self-stabilizing
version of any deterministic solution for the Pattern Formation and the
Gathering problems
Leader Election in Anonymous Rings: Franklin Goes Probabilistic
We present a probabilistic leader election algorithm for anonymous, bidirectional, asynchronous rings. It is based on an algorithm from Franklin, augmented with random identity selection, hop counters to detect identity clashes, and round numbers modulo 2. As a result, the algorithm is finite-state, so that various model checking techniques can be employed to verify its correctness, that is, eventually a unique leader is elected with probability one. We also sketch a formal correctness proof of the algorithm for rings with arbitrary size
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
Survey of Distributed Decision
We survey the recent distributed computing literature on checking whether a
given distributed system configuration satisfies a given boolean predicate,
i.e., whether the configuration is legal or illegal w.r.t. that predicate. We
consider classical distributed computing environments, including mostly
synchronous fault-free network computing (LOCAL and CONGEST models), but also
asynchronous crash-prone shared-memory computing (WAIT-FREE model), and mobile
computing (FSYNC model)
A Taxonomy of Daemons in Self-stabilization
We survey existing scheduling hypotheses made in the literature in
self-stabilization, commonly referred to under the notion of daemon. We show
that four main characteristics (distribution, fairness, boundedness, and
enabledness) are enough to encapsulate the various differences presented in
existing work. Our naming scheme makes it easy to compare daemons of particular
classes, and to extend existing possibility or impossibility results to new
daemons. We further examine existing daemon transformer schemes and provide the
exact transformed characteristics of those transformers in our taxonomy.Comment: 26 page
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