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In this paper we discuss a new knowledgetheoretic definition of agreement appropriate to asynchronous systems. This definition has two important features; first, it uses causality rather than time in its definition and, second, this form of agreement is attainable. In analogy with common knowledge, it is called concurrent common knowledge. Concurrent common knowledge has several applications and we give analyses of two examples that use it. In general, it seems to be the case that applications that involve all processes reaching agreement about some property of a consistent global state are protocols that use concurrent common knowledge.

Concurrent common knowledge: a new definition of agreement for asynchronous systems