We present a tight RMR complexity lower bound for the recoverable mutual exclusion (RME) problem, defined by Golab and Ramaraju \cite{GR2019a}. In particular, we show that any $n$-process RME algorithm using only atomic read, write, fetch-and-store, fetch-and-increment, and compare-and-swap operations, has an RMR complexity of $\Omega(\log n/\log\log n)$ on the CC and DSM model. This lower bound covers all realistic synchronization primitives that have been used in RME algorithms and matches the best upper bounds of algorithms employing swap objects (e.g., [5,6,10]). Algorithms with better RMR complexity than that have only been obtained by either (i) assuming that all failures are system-wide [7], (ii) employing fetch-and-add objects of size $(\log n)^{\omega(1)}$ [12], or (iii) using artificially defined synchronization primitives that are not available in actual systems [6,9].

翻译：对于可回收的相互排斥问题,我们给出了由Golab 和 Ramaraju \ cite{GR2019a} 界定的较紧的RMR复杂性。特别是,我们显示,任何仅使用原子读、写、取和存储、取和催化、以及比较和抽取操作的美元-RME算法,仅使用原子读、写、取和提取、以及比较和交换操作,其RMR复杂性为$-Omega(log n/log\log n) 和 DSM 模型。这一较低约束涵盖所有在RME 算法中使用并符合使用交换对象算法最佳上限(例如[5,6,10] ) 的所有现实同步原始元,或(三) 使用实际系统所不具备的人工定义的同步原始元[6,9] 。