Self-stabilizing local mutual exclusion on networks in which process identifiers are not distinct

A self-stabilizing system is a system such that it autonomously converges to a legitimate system state, regardless of the initial system state. The local mutual exclusion problem is the problem of guaranteeing that no two processes neighboring each other execute their critical sections at a time. The process identifiers are said to be chromatic if no two processes neighboring each other have the same identifiers. Under the assumption that the process identifiers are chromatic, this paper proposes two self-stabilizing local mutual exclusion algorithms; one assumes a tree as the topology of communication network and requires 3 states per process, while the other which works on any communication network, requires n + 1 states per process, where n is the number of processes in the system. We also show that the process identifiers being chromatic is close to necessary for a system to have a self-stabilizing local mutual exclusion algorithm. We adopt the shared memory model for communication and the unfair distributed daemon for process scheduling.