### 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 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### 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

**Brief announcement : Probabilistic stabilization under probabilistic schedulers.** / Yamauchi, Yukiko; Tixeuil, Sébastien; Kijima, Shuji; Yamashita, Masafumi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Distributed Computing - 26th International Symposium, DISC 2012, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7611 LNCS, pp. 413-414, 26th International Symposium on Distributed Computing, DISC 2012, Salvador, Brazil, 10/16/12. https://doi.org/10.1007/978-3-642-33651-5_34

}

TY - GEN

T1 - Brief announcement

T2 - Probabilistic stabilization under probabilistic schedulers

AU - Yamauchi, Yukiko

AU - Tixeuil, Sébastien

AU - Kijima, Shuji

AU - Yamashita, Masafumi

PY - 2012/11/9

Y1 - 2012/11/9

N2 - 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 < ∞.

AB - 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 < ∞.

UR - http://www.scopus.com/inward/record.url?scp=84868348004&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84868348004&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-33651-5_34

DO - 10.1007/978-3-642-33651-5_34

M3 - Conference contribution

AN - SCOPUS:84868348004

SN - 9783642336508

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 413

EP - 414

BT - Distributed Computing - 26th International Symposium, DISC 2012, Proceedings

ER -