MPI-I-95-1-016

In the {\em consensus} problem in a system with $n$ processes, each process starts with a private input value and runs until it chooses irrevocably a decision value, which was the input value of some process of the system; moreover, all processes have to decide on the same value. This work deals with the problem of {\em wait-free} ---fully resilient to processor crash and napping failures--- consensus of $n$ processes in an ``in-phase" multiprocessor system. It proves the existence of a solution to the problem in this system by presenting a protocol which ensures that a process will reach decision within at most $n(n-3)/2 +3$ steps of its own in the worst case, or within $n$ steps if no process fails.