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Marco Realacci 2025-03-18 09:09:12 +01:00
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7
.obsidian/workspace.json vendored
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@ -36,9 +36,9 @@
"type": "pdf", "type": "pdf",
"state": { "state": {
"file": "Concurrent Systems/slides/class 6.pdf", "file": "Concurrent Systems/slides/class 6.pdf",
"page": 2, "page": 3,
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"top": 282, "top": 72,
"zoom": 0.6448931116389548 "zoom": 0.6448931116389548
}, },
"icon": "lucide-file-text", "icon": "lucide-file-text",
@ -220,6 +220,8 @@
}, },
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"Concurrent Systems/notes/6 - Atomicity.md", "Concurrent Systems/notes/6 - Atomicity.md",
"Concurrent Systems/slides/class 5.pdf", "Concurrent Systems/slides/class 5.pdf",
@ -255,7 +257,6 @@
"Concurrent Systems/notes/images/Pasted image 20250304082459.png", "Concurrent Systems/notes/images/Pasted image 20250304082459.png",
"Concurrent Systems/notes/images/Pasted image 20250304093223.png", "Concurrent Systems/notes/images/Pasted image 20250304093223.png",
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"Foundation of data science/notes/1 CV Basics.md", "Foundation of data science/notes/1 CV Basics.md",
"Foundation of data science/notes/7 Autoencoders.md", "Foundation of data science/notes/7 Autoencoders.md",
"Foundation of data science/notes/6 PCA.md", "Foundation of data science/notes/6 PCA.md",

5
Concurrent Systems/notes/6 - Atomicity.md
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@ -14,9 +14,12 @@ A history is **complete** if every inv is eventually followed by a corresponding
### Linearizability ### Linearizability
A complete history $\hat{H}$ is **linearizable** if there exists a sequential history $\hat{S}$ s.t. A complete history $\hat{H}$ is **linearizable** if there exists a sequential history $\hat{S}$ s.t.
- $\forall X :\hat{S}|_{X} \in semantics(X)$ - $\forall X :\hat{S}|_{X} \in semantics(X)$
- $\forall p:\hat{H|_{p} = \hat{S}|p}$ - $\forall p:\hat{H}|_{p} = \hat{S}|p$
- If $res[op] <_{H} inv[op']$, then $res[op] <_{S} inv[op']$ - If $res[op] <_{H} inv[op']$, then $res[op] <_{S} inv[op']$
- can rearrange events only if they overlap - can rearrange events only if they overlap
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.
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