Memory-Anonymous Starvation-Free Mutual Exclusion: Possibility and Impossibility Results

In an anonymous shared memory system, all inter-process communications are via shared objects; however, unlike in standard systems, there is no a priori agreement between processes on the names of shared objects [14,15]. Furthermore, the algorithms are required to be symmetric; that is, the processes should execute precisely the same code, and the only way to distinguish processes is by comparing identifiers for equality. For such a system, read/write registers are called anonymous registers. It is known that symmetric deadlock-free mutual exclusion is solvable for any finite number of processes using anonymous registers [1]. The main question left open in [14,15] is the existence of starvation-free mutual exclusion algorithms for two or more processes. We resolve this open question for memoryless algorithms, in which a process that tries to enter its critical section does not use any information about its previous attempts. Almost all known mutual exclusion algorithms are memoryless. We show that (1) there is a symmetric memoryless starvation-free mutual exclusion algorithm for two processes using $m \geq 7$ anonymous registers if and only if $m$ is odd; and (2) there is no symmetric memoryless starvation-free mutual exclusion algorithm for $n\geq 3$ processes using (any number of) anonymous registers. Our impossibility result is the only example of a system with fault-free processes, where global progress (i.e., deadlock-freedom) can be ensured, while individual progress to each process (i.e., starvation-freedom) cannot. It complements a known result for systems with failure-prone processes, that there are objects with lock-free implementations but without wait-free implementations [2,5].Comment: DISC 2023 versio

Constant RMR Group Mutual Exclusion for Arbitrarily Many Processes and Sessions

Group mutual exclusion (GME), introduced by Joung in 1998, is a natural synchronization problem that generalizes the classical mutual exclusion and readers and writers problems. In GME a process requests a session before entering its critical section; processes are allowed to be in their critical sections simultaneously provided they have requested the same session. We present a GME algorithm that (1) is the first to achieve a constant Remote Memory Reference (RMR) complexity for both cache coherent and distributed shared memory machines; and (2) is the first that can be accessed by arbitrarily many dynamically allocated processes and with arbitrarily many session names. Neither of the existing GME algorithms satisfies either of these two important properties. In addition, our algorithm has constant space complexity per process and satisfies the two strong fairness properties, first-come-first-served and first-in-first-enabled. Our algorithm uses an atomic instruction set supported by most modern processor architectures, namely: read, write, fetch-and-store and compare-and-swap