### Abstract

Motivation. Roughly speaking, a weakly stabilizing system S executed under a probabilistic scheduler ρ is probabilistically self-stabilizing, in the sense that any execution eventually reaches a legitimate execution with probability 1 [1-3]. Here ρ is a set of Markov chains, one of which is selected for S by an adversary to generate as its evolution an infinite activation sequence to execute S. The performance measure is the worst case expected convergence time τ _{S,M} when S is executed under a Markov chain M ∈ ρ. Let τ _{S,ρ} = sup _{Mερ} τ _{S,M}. Then S can be "comfortably" used as a probabilistically self-stabilizing system under ρ only if τ _{S,ρ} < ∞. There are S and ρ such that τ _{S,ρ} = ∞, despite that τ _{S,M} < ∞ for any M ∈ ρ. Somewhat interesting is that, for some S, there is a randomised version S* of S such that τ _{S*,ρ} < ∞, despite that τ _{S,ρ} = ∞, i.e., randomization helps. This motivates a characterization of S that satisfies τ _{S*,ρ} < ∞.

Original language | English |
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Title of host publication | Distributed Computing - 26th International Symposium, DISC 2012, Proceedings |

Pages | 413-414 |

Number of pages | 2 |

DOIs | |

Publication status | Published - Nov 9 2012 |

Event | 26th International Symposium on Distributed Computing, DISC 2012 - Salvador, Brazil Duration: Oct 16 2012 → Oct 18 2012 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7611 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 26th International Symposium on Distributed Computing, DISC 2012 |
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Country | Brazil |

City | Salvador |

Period | 10/16/12 → 10/18/12 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Distributed Computing - 26th International Symposium, DISC 2012, Proceedings*(pp. 413-414). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7611 LNCS). https://doi.org/10.1007/978-3-642-33651-5_34