Knowledge and Common Knowledge in a Distributed Environment

Reasoning about the behavior of distributed algorithms is a difficult task. Without a conceptual framework to encapsulate details, algorithm designers are often forced to resort to proof by cases or ‘manyscenarios’ reasoning to show correctness and impossibility results. As Yemini and Cohen put it, “proving protocols correct (or impossible) is a difficult and cumbersome art in the absence of proper formal tools to reason about protocols. Such backward-induction arguments as the one used in the impossibility proof should require less space and become more convincing with a proper set of tools.” [4] This paper seeks to provide that conceptual framework. By articulating the core of what needs to be proven (possession of knowledge), the authors hope to make the process of reasoning about distributed systems simpler and clearer. The authors’ overall goal is to unify prior and future results in distributed systems under a single body of theory.