@article {IOPORT.06058071,
    author       = {Ben-Zvi, Ido and Moses, Yoram},
    title        = {On interactive knowledge with bounded communication.},
    year         = {2011},
    journal      = {Journal of Applied Non-Classical Logics},
    volume       = {21},
    number       = {3-4},
    issn         = {1166-3081},
    pages        = {323-354},
    publisher    = {Taylor \& Francis},
    doi          = {10.3166/jancl.21.323-354},
    abstract     = {Summary: The effect of upper bounds on message delivery times in a computer network upon the dynamics of knowledge gain is investigated. Recent work has identified centipedes and brooms-causal structures that combine message chains with time bound information-as necessary conditions for knowledge gain and common knowledge gain, respectively. This paper shows that, under the full-information protocol, these structures are both necessary and sufficient for such epistemic gain. We then apply this analysis to gain insights into the relation between ``everyone knows'' and common knowledge. We prove a tight threshold on the depth $k$, beyond which $E^{k} _{G}$ (everyone in $G$ knows nested to depth $k$) collapses into $C_{G}$ (common knowledge), when this knowledge concerns the occurrence of a spontaneous event. The threshold depends on the size of the group $G$ of agents, as well as the time that has elapsed since the event of interest occurred. The existence of such a threshold is not guaranteed for all protocols, which is demonstrated here by presenting a counterexample in which no such threshold exists.},
    identifier   = {06058071},
}