Simple epistemic planning: generalised gossiping

Abstract

The gossip problem, in which information (secrets) must be shared among a certain number of agents using the minimum number of calls, is of interest in the conception of communication networks and protocols. We extend the gossip problem to arbitrary epistemic depths. For example, we may require not only that all agents know all secrets but also that all agents know that all agents know all secrets. We give optimal protocols for the generalised gossip problem, in the case of two-way communications, one-way communications and parallel communication. In the presence of negative goals testing the existence of a successful protocol is NP-complete.