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Marco Realacci 2025-03-18 16:05:04 +01:00
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4
.obsidian/workspace.json vendored
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@ -34,9 +34,9 @@
"type": "pdf", "type": "pdf",
"state": { "state": {
"file": "Concurrent Systems/slides/class 6.pdf", "file": "Concurrent Systems/slides/class 6.pdf",
"page": 4, "page": 5,
"left": -23, "left": -23,
"top": 143, "top": 415,
"zoom": 0.6627078384798101 "zoom": 0.6627078384798101
}, },
"icon": "lucide-file-text", "icon": "lucide-file-text",

3
Concurrent Systems/notes/6 - Atomicity.md
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@ -48,7 +48,8 @@ We now show that $\to$ is acyclic.
- Since $\hat{S}_X$ is a linearization of $\hat{H}|_X$ and op/op' are on X (literally because we have op ->x op'), this implies $res(op') <_X inv(op)$, which means that $op' \to_X op$, and so it won't be a total order... So this is not possible either. - Since $\hat{S}_X$ is a linearization of $\hat{H}|_X$ and op/op' are on X (literally because we have op ->x op'), this implies $res(op') <_X inv(op)$, which means that $op' \to_X op$, and so it won't be a total order... So this is not possible either.
3. It cannot have cycles with more than 2 edges: 3. It cannot have cycles with more than 2 edges:
1. - by contradiction, consider a shortest cycle
- adjacent edges cannot belong to the same order (otw. the cycle would be shortable, because of transitivity)
> [!PDF|red] class 6, p.6> we would have a cycle of length > [!PDF|red] class 6, p.6> we would have a cycle of length