On Proof-Labeling Schemes versus Silent Self-stabilizing Algorithms

Blin, Lélia; Fraigniaud, Pierre; Patt-Shamir, Boaz

doi:10.1007/978-3-319-11764-5_2

Cited by 31 publications

(35 citation statements)

References 19 publications

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“…This can be achieved in the framework of asynchronous systems with transient failures [4]. Our results demonstrate that, conceptually, this can also be achieved in asynchronous systems with crash failures, at low costs, in term of both certificate size and number of opinions.…”

Section: Introductionmentioning

confidence: 59%

“…in distributed complexity [12], in silent selfstabilization [4] (as captured by the concept of proof-labeling schemes [20]), as well as failure detectors [5] where an underlying layer is charged with producing certificates giving information about process failures -the failure detector should provide certificates giving sufficient information about process failures to solve e.g. consensus, but an incorrect certificate should not lead to an invalid consensus solution.…”

Section: Introductionmentioning

confidence: 99%

“…In several of these contexts, one seeks certificates that are as small as possible, perhaps for information theoretic purposes, privacy purposes, or because certificates have to be exchanged among processes [4,20]. As we shall prove in this paper, it is possible to use small certificates to enable the number of opinions to be drastically reduced.…”

Section: Introductionmentioning

confidence: 99%

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Minimizing the Number of Opinions for Fault-Tolerant Distributed Decision Using Well-Quasi Orderings

Fraigniaud

Rajsbaum²,

Travers

2016

LATIN 2016: Theoretical Informatics

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The notion of deciding a distributed language L is of growing interest in various distributed computing settings. Each process p i is given an input value x i , and the processes should collectively decide whether their set of input values x = (x i ) i is a valid state of the system w.r.t. to some specification, i.e., if x ∈ L. In non-deterministic distributed decision each process p i gets a local certificate c i in addition to its input x i . If the input x ∈ L then there exists a certificate c = (c i ) i such that the processes collectively accept x, and if x ∈ L, then for every c, the processes should collectively reject x. The collective decision is expressed by the set of opinions emitted by the processes, and one aims at minimizing the number of possible opinions emitted by each process.In this paper we study non-deterministic distributed decision in asynchronous systems where processes may crash. In this setting, it is known that the number of opinions needed to deterministically decide a language can grow with n, the number of processes in the system. We prove that every distributed language L can be non-deterministically decided using only three opinions, with certificates of size O(log α(n)) bits, where α grows at least as slowly as the inverse of the Ackerman function. The result is optimal, as we show that there are distributed languages that cannot be decided using just two opinions, even with arbitrarily large certificates.To prove our upper bound, we introduce the notion of distributed encoding of the integers, that provides an explicit construction of a long bad sequence in the well-quasi-ordering ({0, 1} * , = ) controlled by the successor function. Thus, we provide a new class of applications for wellquasi-orderings that lies outside logic and complexity theory. For the lower bound we use combinatorial topology techniques.

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Section: Introductionmentioning

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Minimizing the Number of Opinions for Fault-Tolerant Distributed Decision Using Well-Quasi Orderings

Fraigniaud

Rajsbaum²,

Travers

2016

LATIN 2016: Theoretical Informatics

Self Cite

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“…See, e.g., [1] where the notion of local detection was introduced and used for designing a self stabilizing protocol constructing a spanning tree, and [29] for another example of using distributed local verification of proofs for the design of self stabilizing algorithms. The reader interested in the tight connections between proof-labeling schemes and self-stabilization is referred to the recent paper [8]. Proof-labeling schemes, where nodes may communicate at distance greater than 1, i.e., may take their individual decision based on the labels of the nodes in their vicinity at distance t > 1, was recently studied in [20].…”

Section: Related Workmentioning

confidence: 99%

Randomized Proof-Labeling Schemes

Mor

Fraigniaud

Patt-Shamir

2015

Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing

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International audienceA proof-labeling scheme, introduced by Korman, Kutten and Peleg [PODC 2005], is a mechanism enabling to certify the legality of a network configuration with respect to a boolean predicate. Such a mechanism finds applications in many frameworks, including the design of fault-tolerant distributed algorithms. In a proof-labeling scheme, the verification phase consists of exchanging labels between neighbors. The size of these labels depends on the network predicate to be checked. There are predicates requiring large labels, of poly-logarithmic size (e.g., MST), or even polynomial size (e.g., Symmetry). In this paper, we introduce the notion of randomized proof-labeling schemes. By reduction from deterministic schemes, we show that randomization enables the amount of communication to be exponentially reduced. As a consequence, we show that checking any network predicate can be done with probability of correctness as close to one as desired by exchanging just a logarithmic number of bits between neighbors. Moreover, we design a novel space lower bound technique that applies to both deterministic and randomized proof-labeling schemes. Using this technique, we establish several tight bounds on the verification complexity of classical distributed computing problems, such as MST construction, and of classical predicates such as acyclicity, connectivity, and cycle length

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“…However, few works, like [27,28,29], target both general self-stabilizing algorithm patterns and efficiency in rounds.…”

Section: Introductionmentioning

confidence: 99%

Acyclic Strategy for Silent Self-stabilization in Spanning Forests

Altisen

Devismes

Durand

2018

Lecture Notes in Computer Science

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In this paper, we formalize design patterns, commonly used in the self-stabilizing area, to obtain general statements regarding both correctness and time complexity guarantees. Precisely, we study a general class of algorithms designed for networks endowed with a sense of direction describing a spanning forest (e.g., a directed tree or a network where a directed spanning tree is available) whose characterization is a simple (i.e., quasi-syntactic) condition. We show that any algorithm of this class is (1) silent and self-stabilizing under the distributed unfair daemon, and (2) has a stabilization time which is polynomial in moves and asymptotically optimal in rounds. To illustrate the versatility of our method, we review several existing works where our results apply.After the seminal work of Dijkstra, many self-stabilizing algorithms have been proposed to solve various tasks such as spanning tree constructions [2], token circulations [3], clock synchronization [4], propagation of information with feedbacks [5]. Those works consider a large taxonomy of topologies: rings [6,7], (directed) trees [5,8,9], planar graphs [10,11], arbitrary connected graphs [12,13], etc. Among those topologies, the class of directed (in-) trees (i.e., trees where one process is distinguished as the root and edges are oriented toward the root) is of particular interest. Indeed, such topologies often appear, at an intermediate level, in self-stabilizing composite algorithms. Composition is a popular way to design selfstabilizing algorithms [14] since it allows to simplify both the design and proofs. Numerous self-stabilizing algorithms, e.g., [15,2,16], are actually made as a composition of a spanning directed treelike (e.g. tree or forest) construction and some other algorithms specifically designed for directed tree/forest topologies. Notice that, even though not mandatory, most of these constructions achieve an additional property called silence [17]: a silent self-stabilizing algorithm converges within finite time to a configuration from which the values of the communication registers used by the algorithm remain fixed. Silence is a desirable property. Indeed, as noted in [17], the silent property usually implies more simplicity in the algorithm design, and so allows to write simpler proofs; moreover, a silent algorithm may utilize less communication operations and communication bandwidth.In this paper, we consider the locally shared memory model with composite atomicity introduced by Dijkstra [1], which is the most commonly used model in self-stabilization. In this model, executions proceed in (atomic) steps and the asynchrony of the system is captured by the notion of daemon. The weakest (i.e., the most general) daemon is the distributed unfair daemon. Hence, solutions stabilizing under such an assumption are highly desirable, because they work under any other daemon assumption.The daemon assumption and time complexity are closely related. The stabilization time, i.e., the maximum time to reach a legitimate configuration starting f...

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On Proof-Labeling Schemes versus Silent Self-stabilizing Algorithms

Cited by 31 publications

References 19 publications

Minimizing the Number of Opinions for Fault-Tolerant Distributed Decision Using Well-Quasi Orderings

Minimizing the Number of Opinions for Fault-Tolerant Distributed Decision Using Well-Quasi Orderings

Randomized Proof-Labeling Schemes

Acyclic Strategy for Silent Self-stabilization in Spanning Forests

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