Two Consensus Algorithms with Atomic Registers and Failure Detector Omega

We present here two consensus algorithms in shared memory asynchronous systems with the eventual leader election failure detector Ω. In both algorithms eventually only the leader given by failure detector Ω will progress, and being eventually alone to make steps the leader will decide. The first algorithm uses an infinite number of multi-writer multi-reader atomic registers and works with an unbounded number of anonymous processes. The second uses only a finite number of singlewriter multi-reader registers but assumes a finite number of processes with known unique identities.