Local Terminations and Distributed Computability in Anonymous Networks

We investigate the computability of distributed tasks in reliable anonymous networks with arbitrary knowledge. More precisely, we consider tasks computable with local termination, i.e., a node knows when to stop to participate in a distributed algorithm, even though the algorithm is not necessarily terminated elsewhere. We also study weak local termination, that is when a node knows its final value but continues to execute the distributed algorithm, usually in order to provide information to other nodes. We give the first characterization of distributed tasks that can be computed with weak local termination and we present a new characterization of tasks computed with local termination. For both terminations, we also characterize tasks computable by polynomial algorithms.