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# Causality

Last updated May 5, 2022

## # Causality

• When $a \rightarrow b$ then $a$ might have caused $b$
• We say event $a$ happens before event $b$ ($a \rightarrow b$) iff:
• $a$ and $b$ occurred at the same node, and $a$ occurred before $b$ in that node’s local execution order
• $a$ is the sending of some message $m$ and $b$ is the receipt of that same message $m$ (assuming sent messages are unique)
• there exists some $c$ such that $a \rightarrow c$ and $c \rightarrow b$

## # Concurrency

• When $a \parallel b$ then $a$ cannot have cause $b$ (and vice versa)
• Concurrent does not mean simultaneous, it means two things did not know about each other when they occurred (a is concurrent with b is written as $a \parallel b$)

## # Causal Order

• $\prec$ is a causal order, it is consistent with causality, a strict total order on events