On knowledge and communication complexity in distributed systems

Abstract

This paper contributes to exploring the connection between epistemic knowledge and communication complexity in distributed systems. We focus on Action Models, a well-known variant of dynamic epistemic logic, which allows to cleanly separate the state of knowledge of the processes and its update due to communication actions: Exactly like the set of possible global states, the possible actions are described by means of a Kripke model that specifies which communication actions are indistinguishable for which process. We first show that the number of connected components in the action model results in a lower bound for communication complexity. We then apply this result, in the restricted setting of a two processor system, for determining communication complexity lower bounds for solving a distributed computing problem P: We first determine some properties of the action model corresponding to any given protocol that solves P, and then use our action model communication complexity lower bounds. Finally, we demonstrate our approach by applying it to synchronous distributed function computation and to a simple instance of consensus in directed dynamic networks.