匿名无障碍$(n,k)$ -设置与$n-k+1$原子读/写寄存器的一致性
Anonymous Obstruction-free $(n,k)$-Set Agreement with $n-k+1$ Atomic Read/Write Registers
摘要：
$k$ -集合一致性问题是一致性问题的推广。即，假设每个过程提出一个值，每个非故障过程必须决定一个值，使得每个决定的值被提出，并且不超过$k$不同的值被决定。这是一个难题，因为在异步系统中，一旦$k$或多个进程崩溃，就无法解决这个问题。规避这种不可能性的一种方法是削弱其终止属性，要求进程只有在足够长的时间内单独执行时才终止（决定）。这就是著名的无障碍进展条件。考虑一个由$n$ { \it anonymous asynchronous}进程组成的系统，其中进程之间通过原子寄存器进行通信，并且其中任意数目的进程都可能崩溃，本文提出并解决了一个具有挑战性的公开问题：设计一个仅使用$(n-k+1)$原子寄存器的无障碍$k$ -集合协商算法.从共享内存成本的角度来看，该算法是迄今为止已知的最佳算法，从而建立了解决问题所需的寄存器数量的新上限（相对于先前的上限，其增益为$(n-k)$）。该算法，然后扩展到解决重复版本的$(n,k)$ -集协议。由于它是最佳的原子读/写寄存器的数量，该算法关闭了以前建立的下/上界的差距为匿名和非匿名版本的重复$(n,k)$ -集协议问题。最后，对于$1 \leq x\leq k \textless{} n$，还描述了适合于$x$的推广--无障碍，其仅需要$(n-k+x)$原子寄存器。
英文摘要：
The $k$-set agreement problem is a generalization of the consensus problem. Namely, assuming each process proposes a value, each non-faulty process has to decide a value such that each decided value was proposed, and no more than $k$ different values are decided. This is a hard problem in the sense that it cannot be solved in asynchronous systems as soon as $k$ or more processes may crash. One way to circumvent this impossibility consists in weakening its termination property, requiring that a process terminates (decides) only if it executes alone during a long enough period. This is the well-known obstruction-freedom progress condition. Considering a system of $n$ {\it anonymous asynchronous} processes, which communicate through atomic {\it read/write registers only}, and where {\it any number of processes may crash}, this paper addresses and solves the challenging open problem of designing an obstruction-free $k$-set agreement algorithm with $(n-k+1)$ atomic registers only. From a shared memory cost point of view, this algorithm is the best algorithm known so far, thereby establishing a new upper bound on the number of registers needed to solve the problem (its gain is $(n-k)$ with respect to the previous upper bound). The algorithm is then extended to address the repeated version of $(n,k)$-set agreement. As it is optimal in the number of atomic read/write registers, this algorithm closes the gap on previously established lower/upper bounds for both the anonymous and non-anonymous versions of the repeated $(n,k)$-set agreement problem. Finally, for $1 \leq x\leq k \textless{} n$, a generalization suited to $x$-obstruction-freedom is also described, which requires $(n-k+x)$ atomic registers only.
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。
