Converging on Common Knowledge

Common knowledge, as is well known, is not attainable in finite time by unreliable communication, thus hindering perfect coordination. Focusing on the coordinated attack problem modeled using dynamic epistemic logic, this paper discusses unreliable communication protocols from a topological perspective and asks "If the generals may communicate indefinitely, will they then *converge* to a state of common knowledge?" We answer by making precise and showing the following: *common knowledge is attainable if, and only if, we do not care about common knowledge*.