L-弹性与等待自由的碰集关系
Relating L-Resilience and Wait-Freedom via Hitting Sets
摘要：
t-resilience的条件规定，一个n-process程序只有在至少n-t个进程正确时才有义务取得进展。换句话说，活的集合，进程集合的集合，如果其中一个集合中的所有进程都是正确的，则需要进度，所有集合都至少有n-t个进程。我们发现，任意收集的活集L解决分布式任务的能力是密切相关的最小命中集的L，一个最小的基数子集的进程，有一个非空的交集与每个活集。因此，求L的计算能力是NP完全的。对于允许参与过程相互采用输入或输出值的无色任务的特殊情况，我们使用一个简单的模拟来证明一个任务可以L-弹性地解决当且仅当它可以（h-1）-弹性地解决，其中h是L的最小命中集的大小。对于一般的任务，我们的特征L-弹性可解性的任务相对于一个有限的概念弱可解性：在每一个执行中，所有的过程中的一些集合在L是正确的，输出必须产生的每个过程中的一些（可能不同的）参与集在L。给定一个任务T，我们构造另一个任务T_L，使得T是弱L-弹性可解的当且仅当T_L是弱等待自由可解的。
英文摘要：
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. We show that the ability of arbitrary collection of live sets 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, finding the computing power of L is NP-complete. For the special case of colorless tasks that allow participating processes to adopt input or output values of each other, we use a simple simulation to show that a task can be solved L-resiliently if and only if it can be solved (h-1)-resiliently, where h is 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_L such that T is solvable weakly L-resiliently if and only if T_L is solvable weakly wait-free.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
