@techreport{GK-OLAHSCT-tr-10,
Title = {On L-Resilient Adversaries, Hitting Sets and Colorless Tasks},
Author = {Gafni, Eli and Kuznetsov, Petr},
Year = {2010},
Note = {arXiv:1004.4701},
Type = {Technical Report},
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 {\it 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 {\it 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 {\it 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 {\it 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 {\it 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.},
Url = {http://arxiv.org/abs/1004.4701},
Categories = {tlabs_yes, group_feldmann},
Projectname = {distributed_systems and thisisimportant}
}