2009 **Abstract:** In this article, we show that some fundamental self-and snap-stabilizing wave protocols (e.g., token circulation, PIF, etc.) implicitly assume a very light property that we call BreakingIn. We prove that BreakingIn is strictly induced by self-and snap-stabilization. Combined with a transformer, BreakingIn allows to easily turn the non-fault-tolerant versions of those protocols into snap-stabilizing versions. Unlike the previous solutions, the transformed protocols are very efficient and work at least with the …

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“…To obtain such a token circulation, one can compose a selfstabilizing leader election algorithm (e.g., in [1], [13], [15]) with one of the self-stabilizing token circulation algorithms in [9], [10], [12], [17] for arbitrary rooted networks. The composition only consists of two algorithms running concurrently with the following rule: if a process decides that it is the leader, it executes the root code of the token circulation.…”

confidence: 99%

“…We assume that T C is a fair composition of the token circulation algorithm in [10] and the leader election algorithm in [13]. It follows that the following properties hold: (1) starting from any configuration, there is a unique token in the distributed system in O(n) rounds, and (2) once there is a unique token, O(n) processes can receive the token before a process receives the token.…”

confidence: 99%

“…The second definition of snap-stabilization describes a snapstabilizing program as immediately satisfying an external invocation (such as waves in [6], [7], [8]). Such approach may lead to specifications with sequence-based safety and liveness properties.…”

confidence: 99%

“…Generally, this resource corresponds to a set of shared variables in a common store or a shared hardware device (e.g., a printer). The first snap-stabilizing implementation of mutual exclusion is presented in [21] but in the state model (a stronger model than the message-passing model). In [21], authors adopt the following specification 4 :…”

confidence: 99%

“…To our knowledge, until now, only two works [31,32] conciliate general schemes for stabilization and efficiency in both moves and rounds. In [31], Cournier et al propose a general scheme for snap-stabilizing wave, henceforth non-silent, algorithms in arbitrary connected and rooted networks. Using their approach, one can obtain snap-stabilizing algorithms that execute each wave in polynomial number of rounds and moves.…”

confidence: 99%