From 9322e5e2735e208a79b3e5202b6ed91af80aac9a Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Tue, 18 Mar 2025 16:15:04 +0100 Subject: [PATCH] vault backup: 2025-03-18 16:15:04 --- Concurrent Systems/notes/6 - Atomicity.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/Concurrent Systems/notes/6 - Atomicity.md b/Concurrent Systems/notes/6 - Atomicity.md index d4f1ed9..c916083 100644 --- a/Concurrent Systems/notes/6 - Atomicity.md +++ b/Concurrent Systems/notes/6 - Atomicity.md @@ -49,7 +49,9 @@ We now show that $\to$ is acyclic. 3. It cannot have cycles with more than 2 edges: - by contradiction, consider a shortest cycle - - adjacent edges cannot belong to the same order (not both $\to_X$ ), otw. the cycle would be shortable, because of transitivity of the total order! + - adjacent edges cannot belong to the same order (e.g. not both $\to_X$), otw. the cycle would be shortable, because of transitivity of the total order! + - adjacent edges cannot belong to orders on different objects + - this would mean that an operation is involved in both $\to_X$ and $\to_Y$ > [!PDF|red] class 6, p.6> we would have a cycle of length