The weakest failure detector to solve the mutual exclusion problem in an unknown dynamic environment

Mutual exclusion is one of the fundamental problems in distributed computing but existing mutual exclusion algorithms are unadapted to the dynamics and lack of membership knowledge of current distributed systems (e.g., mobile ad-hoc networks, peer-to-peer systems, etc.). Additionally, in order to circumvent the impossibility of solving mutual exclusion in asynchronous message passing systems where processes can crash, some solutions include the use of (T + Σl) [3], which is the weakest failure detector to solve mutual exclusion in known static distributed systems. In this paper, we define a new failure detector TΣlr which is equivalent to (T + Σl) in known static systems, and prove that T Σlr is the weakest failure detector to solve mutual exclusion in unknown dynamic systems with partial memory losses. We consider that crashed processes may recover.