Brief announcement: early decision despite general process omission failures

In the consensus problem, each process proposes a value and the non-faulty processes have to decide (termination) on the same value (agreement) that has to be one of the proposed values (validity). Two versions of the consensus problem are usually distinguished. They differ in the statement of the agreement property. In the non-uniform version (consensus), agreement is only required on the non-faulty processes (this means that faulty processes are allowed to decide values different from the value decided by the nonfaulty processes). In the uniform version (uniform consensus), agreement concerns all the processes that decide, no two processes (be them faulty or not) can decide differently. Synchronous systems provide upper bounds on processing time and communication delays. Those bounds allow consensus problems to be solved. Basically, a distributed synchronous consensus protocol proceeds by successive rounds. During each round the processes exchange values until they attain a round during which they can conclude that they have converged to the same value. Consensus protocols in synchronous systems are characterized by the failure model they address~ the maximal number of processes they allow to be faulty, and the maximal number of rounds they need to attain a decision. Three failure models have been investigated: the crash model where processes can fail by prematurely halting, the omission model where processes can fail by halting or omitting to send or receive messages they should, and the Byzantine model where processes can fail by exhibiting arbitrary behavior. These failure models are of increasing severity. Let n and t denote the total number of processes and the maximum number of processes that can be faulty, respectively. We have: • Crash failure model: both consensus and uniform consensus can be solved for any value of t (i.e., for t < n), • Omission failure model: consensus can be solved for any t, while uniform consensus requires t < n/2, • Byzantine failure model: consensus can be solved provided that t < n/3. (Uniform consensus is meaningless in that model.) It has been shown that t + 1 is a lower bound on the