Brief Announcement: Space-Optimal Naming in Population Protocols

This paper gives a brief presentation of a comprehensive study on the necessary and sufficient state space conditions for the deterministic naming task in the population protocol model. This problem is studied under various combinations of model assumptions: weak or global fairness, arbitrary or uniform initialization of agents, existence or absence of a distinguishable agent (arbitrarily initialized or not), possibility of breaking symmetry in pair-wise interactions (symmetric or asymmetric transitions). For each possible combination of these assumptions, either an impossibility is proven or the necessary exact number of states (per mobile agent) is determined and an appropriate space-optimal naming protocol is given.