From e9ad07bfd4186991dcea31851964bf3a76c797a5 Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Tue, 18 Mar 2025 16:20:04 +0100 Subject: [PATCH] vault backup: 2025-03-18 16:20:04 --- .obsidian/workspace.json | 2 +- Concurrent Systems/notes/6 - Atomicity.md | 4 +++- 2 files changed, 4 insertions(+), 2 deletions(-) diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index c1c26a8..2bcc1c5 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -36,7 +36,7 @@ "file": "Concurrent Systems/slides/class 6.pdf", "page": 5, "left": -23, - "top": 415, + "top": 360, "zoom": 0.6627078384798101 }, "icon": "lucide-file-text", diff --git a/Concurrent Systems/notes/6 - Atomicity.md b/Concurrent Systems/notes/6 - Atomicity.md index c916083..9a7d052 100644 --- a/Concurrent Systems/notes/6 - Atomicity.md +++ b/Concurrent Systems/notes/6 - Atomicity.md @@ -51,7 +51,9 @@ We now show that $\to$ is acyclic. - by contradiction, consider a shortest cycle - 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 $\to_Y$ + - this would mean that an operation is involved in both $\to_X$ and $\to_Y$ but it is not possible of course + - Hence, at least one $\to_X$ exists and it must be between two $\to_H$ i.e.: $$op1 \to_H op2 \to_X op3 \to_H op4$$ + - can this be a cycle? > [!PDF|red] class 6, p.6> we would have a cycle of length