#### Tight Lower Bounds for the RMR Complexity of Recoverable Mutual Exclusion

##### David Yu Cheng Chan, Philipp Woelfel

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].

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