1,037 research outputs found

    Dynamic FTSS in Asynchronous Systems: the Case of Unison

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    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

    Minimizing Message Size in Stochastic Communication Patterns: Fast Self-Stabilizing Protocols with 3 bits

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    This paper considers the basic PULL\mathcal{PULL} model of communication, in which in each round, each agent extracts information from few randomly chosen agents. We seek to identify the smallest amount of information revealed in each interaction (message size) that nevertheless allows for efficient and robust computations of fundamental information dissemination tasks. We focus on the Majority Bit Dissemination problem that considers a population of nn agents, with a designated subset of source agents. Each source agent holds an input bit and each agent holds an output bit. The goal is to let all agents converge their output bits on the most frequent input bit of the sources (the majority bit). Note that the particular case of a single source agent corresponds to the classical problem of Broadcast. We concentrate on the severe fault-tolerant context of self-stabilization, in which a correct configuration must be reached eventually, despite all agents starting the execution with arbitrary initial states. We first design a general compiler which can essentially transform any self-stabilizing algorithm with a certain property that uses \ell-bits messages to one that uses only log\log \ell-bits messages, while paying only a small penalty in the running time. By applying this compiler recursively we then obtain a self-stabilizing Clock Synchronization protocol, in which agents synchronize their clocks modulo some given integer TT, within O~(lognlogT)\tilde O(\log n\log T) rounds w.h.p., and using messages that contain 33 bits only. We then employ the new Clock Synchronization tool to obtain a self-stabilizing Majority Bit Dissemination protocol which converges in O~(logn)\tilde O(\log n) time, w.h.p., on every initial configuration, provided that the ratio of sources supporting the minority opinion is bounded away from half. Moreover, this protocol also uses only 3 bits per interaction.Comment: 28 pages, 4 figure

    Randomization Adaptive Self-Stabilization

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    We present a scheme to convert self-stabilizing algorithms that use randomization during and following convergence to self-stabilizing algorithms that use randomization only during convergence. We thus reduce the number of random bits from an infinite number to a bounded number. The scheme is applicable to the cases in which there exits a local predicate for each node, such that global consistency is implied by the union of the local predicates. We demonstrate our scheme over the token circulation algorithm of Herman and the recent constant time Byzantine self-stabilizing clock synchronization algorithm by Ben-Or, Dolev and Hoch. The application of our scheme results in the first constant time Byzantine self-stabilizing clock synchronization algorithm that uses a bounded number of random bits

    Fast self-stabilizing byzantine tolerant digital clock synchronization

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    Consider a distributed network in which up to a third of the nodes may be Byzantine, and in which the non-faulty nodes may be subject to transient faults that alter their memory in an arbitrary fashion. Within the context of this model, we are interested in the digital clock synchronization problem; which consists of agreeing on bounded integer counters, and increasing these counters regularly. It has been postulated in the past that synchronization cannot be solved in a Byzantine tolerant and self-stabilizing manner. The first solution to this problem had an expected exponential convergence time. Later, a deterministic solution was published with linear convergence time, which is optimal for deterministic solutions. In the current paper we achieve an expected constant convergence time. We thus obtain the optimal probabilistic solution, both in terms of convergence time and in terms of resilience to Byzantine adversaries

    An Optimal Self-Stabilizing Firing Squad

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    Consider a fully connected network where up to tt processes may crash, and all processes start in an arbitrary memory state. The self-stabilizing firing squad problem consists of eventually guaranteeing simultaneous response to an external input. This is modeled by requiring that the non-crashed processes "fire" simultaneously if some correct process received an external "GO" input, and that they only fire as a response to some process receiving such an input. This paper presents FireAlg, the first self-stabilizing firing squad algorithm. The FireAlg algorithm is optimal in two respects: (a) Once the algorithm is in a safe state, it fires in response to a GO input as fast as any other algorithm does, and (b) Starting from an arbitrary state, it converges to a safe state as fast as any other algorithm does.Comment: Shorter version to appear in SSS0

    Universal Loop-Free Super-Stabilization

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    We propose an univesal scheme to design loop-free and super-stabilizing protocols for constructing spanning trees optimizing any tree metrics (not only those that are isomorphic to a shortest path tree). Our scheme combines a novel super-stabilizing loop-free BFS with an existing self-stabilizing spanning tree that optimizes a given metric. The composition result preserves the best properties of both worlds: super-stabilization, loop-freedom, and optimization of the original metric without any stabilization time penalty. As case study we apply our composition mechanism to two well known metric-dependent spanning trees: the maximum-flow tree and the minimum degree spanning tree

    A Self-Stabilizing Hybrid Fault-Tolerant Synchronization Protocol

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    This paper presents a strategy for solving the Byzantine general problem for self-stabilizing a fully connected network from an arbitrary state and in the presence of any number of faults with various severities including any number of arbitrary (Byzantine) faulty nodes. The strategy consists of two parts: first, converting Byzantine faults into symmetric faults, and second, using a proven symmetric-fault tolerant algorithm to solve the general case of the problem. A protocol (algorithm) is also present that tolerates symmetric faults, provided that there are more good nodes than faulty ones. The solution applies to realizable systems, while allowing for differences in the network elements, provided that the number of arbitrary faults is not more than a third of the network size. The only constraint on the behavior of a node is that the interactions with other nodes are restricted to defined links and interfaces. The solution does not rely on assumptions about the initial state of the system and no central clock nor centrally generated signal, pulse, or message is used. Nodes are anonymous, i.e., they do not have unique identities. A mechanical verification of a proposed protocol is also present. A bounded model of the protocol is verified using the Symbolic Model Verifier (SMV). The model checking effort is focused on verifying correctness of the bounded model of the protocol as well as confirming claims of determinism and linear convergence with respect to the self-stabilization period

    A Self-Stabilizing Hybrid-Fault Tolerant Synchronization Protocol

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    In this report we present a strategy for solving the Byzantine general problem for self-stabilizing a fully connected network from an arbitrary state and in the presence of any number of faults with various severities including any number of arbitrary (Byzantine) faulty nodes. Our solution applies to realizable systems, while allowing for differences in the network elements, provided that the number of arbitrary faults is not more than a third of the network size. The only constraint on the behavior of a node is that the interactions with other nodes are restricted to defined links and interfaces. Our solution does not rely on assumptions about the initial state of the system and no central clock nor centrally generated signal, pulse, or message is used. Nodes are anonymous, i.e., they do not have unique identities. We also present a mechanical verification of a proposed protocol. A bounded model of the protocol is verified using the Symbolic Model Verifier (SMV). The model checking effort is focused on verifying correctness of the bounded model of the protocol as well as confirming claims of determinism and linear convergence with respect to the self-stabilization period. We believe that our proposed solution solves the general case of the clock synchronization problem
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