Optimal Memory-Anonymous Symmetric Deadlock-Free Mutual Exclusion

The notion of an anonymous shared memory, introduced by Taubenfeld in PODC 2017, considers that processes use different names for the same memory location. As an example, a location name A used by a process p and a location name B ≠ A used by another process q can correspond to the very same memory location X, and similarly for the names B used by p and A used by q which may (or may not) correspond to the same memory location Y ≠ X. In this context, the PODC paper presented a 2-process symmetric deadlock-free mutual exclusion (mutex) algorithm and a necessary condition on the size m of the anonymous memory for the existence of such an n-process algorithm. This condition states that m must be belongs to M(n) {1} where M(n)= {m: ∀ ℓ: (1) < ℓ ≤ n: gcd(ℓ,m)=1). Symmetric means here that,process identities define a specific data type which allows a process to check only if two identities are equal or not.