Reachability of Five Gossip Protocols

Gossip protocols use point-to-point communication to spread information within a network until every agent knows everything. Each agent starts with her own piece of information (‘secret’) and in each call two agents will exchange all secrets they currently know. Depending on the protocol, this leads to different distributions of secrets among the agents during its execution. We investigate which distributions of secrets are reachable when using several distributed epistemic gossip protocols from the literature. Surprisingly, a protocol may reach the distribution where all agents know all secrets, but not all other distributions. The five protocols we consider are called 햠햭햸, 햫햭햲, 햢햮, 햳햮햪, and 햲햯햨. We find that 햳햮햪 and 햠햭햸 reach the same distributions but all other protocols reach different sets of distributions, with some inclusions. Additionally, we show that all distributions are subreachable with all five protocols: any distribution can be reached, if there are enough additional agents

Temporal Epistemic Gossip Problems

International audienceGossip problems are planning problems where several agents have to share information (`secrets') by means of phone calls between two agents. In epistemic gossip problems the goal can be to achieve higher-order knowledge, i.e., knowledge about other agents' knowledge; to that end, in a call agents communicate not only secrets, but also agents' knowledge of secrets, agents' knowledge about other agents' knowledge about secrets, etc. Temporal epistemic gossip problems moreover impose constraints on the times of calls. These constraints are of two kinds: either they stipulate that a call between two agents must necessarily be made at some time point, or they stipulate that a call can be made within some possible (set of) interval(s). In the non-temporal version, calls between two agents are either always possible or always impossible. We investigate the complexity of the plan existence problem in this general setting. Concerning the upper bound, we prove that it is in NP in the general case, and that it is in P when the problem is non-temporal and the goal is a positive epistemic formula. As for the lower bound, we prove NP-completeness for two fragments: problems with possibly negative goals even in the non-temporal case, and problems with temporal constraints even if the goal is a set of positive atoms