From 32053062f6a0311811d09f6dbc767206af88db8d Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Tue, 18 Mar 2025 16:35:04 +0100 Subject: [PATCH] vault backup: 2025-03-18 16:35:04 --- Concurrent Systems/notes/6 - Atomicity.md | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/Concurrent Systems/notes/6 - Atomicity.md b/Concurrent Systems/notes/6 - Atomicity.md index 0057b81..0827fae 100644 --- a/Concurrent Systems/notes/6 - Atomicity.md +++ b/Concurrent Systems/notes/6 - Atomicity.md @@ -56,8 +56,11 @@ We now show that $\to$ is acyclic. - can this be a cycle? - $op1 \to_H op2$ means that $res(op1) <_H inv(op2)$ - $op2 \to_X op3$ entails that $inv(op2) <_H res(op3)$ - - if not, as is a total order, we would have that $res(op3) <_H inv(op2)$, but we then would have $op3 \to_H op2$ a cycle of lenght 2... - - $op2 \to_H op3$ entails that $inv(op2) <_H res(op3)$ + - if not, as is a total order, we would have that $res(op3) <_H inv(op2)$, but we then would have $op3 \to_H op2$, forming a cycle of lenght 2 because $op2 \to_X op3$, and we know cycles of lenght 2 are not possible... + - $op3 \to_H op4$ means that $res(op3) <_H inv(op4)$ + + - We would then have that $res(op1) <_H inv(op2) <_H res(op3) <_H inv(op4)$ + - So by transitivity $res(op1) <_H inv(op4)$ > [!PDF|red] class 6, p.6> we would have a cycle of length