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I am reading Fischer, Michael J., Nancy A. Lynch, and Michael S. Paterson. "Impossibility of distributed consensus with one faulty process." Journal of the ACM (JACM) 32.2 (1985): 374-382, available here, the paper in which the well known FLP Theorem was proved.

I am having trouble understanding the notion of an "applicable event" used in this paper. Here's a quote from the paper (Section 2):

Since processes are deterministic, the step is completely determined by the pair $e = (p,m)$, which we call an event. (This "event" should be thought of as the receipt of $m$ by $p$.) $e(C)$ denotes the resulting configuration, and we say that $e$ can be applied to $C$.

I can't understand this definition. When is an event applicable? When is it not applicable?

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An event $e$ is applicable in configuration $C$ if it could happen at configuration $C$. Since $e = (p,m)$ means that message $m$ arrives at processor $p$, $e$ is applicable at $C$ if the message queue at $C$ contains the message $m$ directed at $p$. If there is no message directed at $p$ with contents $m$ then $e$ is not applicable at $C$.

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  • $\begingroup$ Ah, I see. This makes sense. I'll wait a few more hours before accepting your answer just in case an even better answer shows up. $\endgroup$ – Jacopo Notarstefano Nov 15 '14 at 23:18

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