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We present the first recoverable mutual exclusion (RME) algorithm that issimultaneously abortable, adaptive to point contention, and with sublogarithmicRMR complexity. Our algorithm has $O(\min(K,\log_W N))$ RMR passage complexityand $O(F + \min(K,\log_W N))$ RMR super-passage complexity, where $K$ is thenumber of concurrent processes (point contention), $W$ is the size (in bits) ofregisters, and $F$ is the number of crashes in a super-passage. Under thestandard assumption that $W=\Theta(\log N)$, these bounds translate toworst-case $O(\frac{\log N}{\log \log N})$ passage complexity and $O(F +\frac{\log N}{\log \log N})$ super-passage complexity. Our key building blocksare:  * A $D$-process abortable RME algorithm, for $D \leq W$, with $O(1)$ passagecomplexity and $O(1+F)$ super-passage complexity. We obtain this algorithm byusing the Fetch-And-Add (FAA) primitive, unlike prior work on RME that usesFetch-And-Store (FAS/SWAP).  * A generic transformation that transforms any abortable RME algorithm withpassage complexity of $B < W$, into an abortable RME lock with passagecomplexity of $O(\min(K,B))$.

Recoverable, Abortable, and Adaptive Mutual Exclusion with Sublogarithmic RMR Complexity