From ccfb975479892aeecc4e95d3d6f598d0c000c6d2 Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Tue, 25 Mar 2025 15:42:22 +0100 Subject: [PATCH] vault backup: 2025-03-25 15:42:22 --- .obsidian/workspace.json | 4 ++-- Concurrent Systems/notes/8 - Enhancing Liveness Properties.md | 4 ++-- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 115a40a..1600c2c 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -6,7 +6,7 @@ { "id": "efd2410a71337f52", "type": "tabs", - "dimension": 85.67335243553008, + "dimension": 64.46991404011462, "children": [ { "id": "383fb8ddbc7a9dc8", @@ -42,7 +42,7 @@ { "id": "496ffcebad48669d", "type": "tabs", - "dimension": 14.326647564469914, + "dimension": 35.53008595988539, "children": [ { "id": "879210c00db77468", diff --git a/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md b/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md index d13cbb3..5aa3db9 100644 --- a/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md +++ b/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md @@ -36,8 +36,8 @@ stop_help(i) := *Proof:* By contr., $\exists \tau$ s.t. $\exists$ many (> 0) op.'s invoked concurrently that never terminate. Let Q be the set of proc.'s that performed these invocations. -- by enrichment, eventually `NEED_HELP[i]=T` ($\forall i\in Q$) forever -- since crashed are fail-stop, eventually `NEED_HELP[j]` is no longer modified ($\forall j \not \in Q$) +- by enrichment, eventually `NEED_HELP[i]=T` forever ($\forall i\in Q$) +- since crashes are fail-stop, eventually `NEED_HELP[j]` is no longer modified ($\forall j \not \in Q$) - $\exists \tau' \geq \tau$ where all proc.'s in Q compute the same X **Observation:** $Q \subseteq X$ (it is possible that $p_j$ sets `NEED_HELP[j]` and then fails)