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# Publications by Type: Technical Reports

Citation key | GK-OLAHSCT-tr-10 |
---|---|

Author | Gafni, Eli and Kuznetsov, Petr |

Year | 2010 |

Note | arXiv:1004.4701 |

Institution | arXiv.org |

Abstract | The
condition of t-resilience stipulates that an n-process program is only
obliged to make progress when at least n-t processes are correct. Put
another way, the live sets, the collection of process sets such
that progress is required if all the processes in one of these sets
are correct, are all sets with at least n-t processes. In this paper
we study what happens when the live sets are any arbitrary collection
of sets L. We show that the power of L to solve distributed tasks is
tightly related to the minimum hitting set of L, a minimum
cardinality subset of processes that has a non-empty intersection with
every live set. Thus, a necessary condition to make progress in the
presence of L is that at least one member of the set is correct. For
the special case of colorless tasks that allow participating
processes to adopt input or output values of each other, we show that
the set of tasks that can be solved L-resiliently is exactly
captured by the size of the minimum hitting set of L. For general
tasks, we characterize L-resilient solvability of tasks with respect
to a limited notion of weak solvability: in every execution
where all processes in some set in L are correct, outputs must be
produced for every process in some (possibly different) participating
set in L. Given a task T, we construct another task T' such that T is
solvable weakly L-resiliently if and only if T' is solvable weakly
wait-free. |

Bibtex Type of Publication | Technical Report |

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