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Concurrent Systems/notes/6 - Atomicity.md
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@ -21,9 +21,9 @@ A complete history $\hat{H}$ is **linearizable** if there exists a sequential hi
Given an history $\hat{K}$, we can define a binary relation on events $⟶_{K}$ s.t. (op, op’) ∈ ⟶K if and only if res[op] <K inv[op’]. We write op ⟶K op’ for denoting (op, op’) ∈ ⟶K. Hence, condition 3 of the previous Def. requires that ⟶H ⊆ ⟶S.
![[/Concurrent Systems/notes/images/Pasted image 20250318090733.png]]
![](Concurrent%20Systems/notes/images/Pasted%20image%2020250318090733.png)
![[/Concurrent Systems/notes/images/Pasted image 20250318090909.png]]But there is another linearization possible! I can also push a before if I pull it before c!
![](Concurrent%20Systems/notes/images/Pasted%20image%2020250318090909.png)But there is another linearization possible! I can also push a before if I pull it before c!
Of course I have to respect the semantics of a Queue (if I push "a" first, I have to pop "a" first because it's a fucking FIFO)
#### Compositionality theorem