Tight Group Renaming on Groups of Size g Is Equivalent to g-Consensus

This thesis addresses the relations between two problems in distributed computing, the g-tight group renaming task and what we call, safe-consensus task. We show that the g-tight group renaming task implements g processes consensus by introducing an intermediate task, the safeconsensus task. We provide an implementation of g-safe-consensus from g-tight group renaming and an implementation of g-consensus from the former. It is known that with g-consensus g-tight group renaming is solvable, thus we close the loop and prove that the two problems are equivalent. The safe-consensus task, is of independent interest. In it the validity condition of consensus is weakened as follows: if the first processor to invoke the task returns before any other processor invokes, i.e., it runs in solo, then it outputs its input; Otherwise the consensus output can be arbitrary, not even the input of any process. We show the equivalence between safe-(set)-consensus and (set)-consensus.