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

TL;DR

This paper investigates the possibility of starvation-free mutual exclusion in anonymous shared memory systems, providing new impossibility and possibility results for different process counts and register conditions.

Contribution

It establishes the first results characterizing when symmetric memoryless starvation-free mutual exclusion is possible or impossible in anonymous systems.

Findings

A symmetric memoryless starvation-free mutual exclusion algorithm exists for two processes with an odd number of registers ≥7.

No such algorithm exists for three or more processes, regardless of the number of registers.

The results highlight fundamental limitations of anonymous shared memory systems for mutual exclusion.

Abstract

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].