Concurrent common knowledge: defining agreement for asynchronous systems

Abstract

In this paper we present a new, knowledge-theoretic definition of agreement designed for asynchronous systems. In analogy with common knowledge, it is called concurrent common knowledge. Unlike common knowledge, it is a form of agreement that is attainable asynchronously. In defining concurrent common knowledge, we give a logic with new modal operators and a formal semantics, both of which are based on causality and consequently capture only the relevant structure of purely asynchronous systems. We give general conditions by which protocols attain concurrent common knowledge and prove that two simple and efficient protocols do so. We also present several applications of our logic. We show that concurrent common knowledge is a necessary and sufficient condition for the concurrent performance of distributed actions. We also demonstrate the role of knowledge in taking snapshots for stable property detection and asynchronous broadcasts. In general, applications that involve all processes reaching agreement about some porperty of a consistent global state can be understood in terms of concurrent common knowledge.