From 124d580bad81836e0d84577ad638423d7cea71ad Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Tue, 25 Mar 2025 09:23:01 +0100 Subject: [PATCH] vault backup: 2025-03-25 09:23:01 --- .obsidian/workspace.json | 4 ++-- .../notes/8 - Enhancing Liveness Properties.md | 5 ++++- 2 files changed, 6 insertions(+), 3 deletions(-) diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 933d7f2..1b5d982 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -229,10 +229,10 @@ "companion:Toggle completion": false } }, - "active": "0d64f519fd7f9420", + "active": "879210c00db77468", "lastOpenFiles": [ - "Concurrent Systems/slides/class 8.pdf", "Concurrent Systems/notes/8 - Enhancing Liveness Properties.md", + "Concurrent Systems/slides/class 8.pdf", "Pasted image 20250325090735.png", "Concurrent Systems/notes/7- MUTEX-free concurrency.md", "Concurrent Systems/notes/images/Pasted image 20250324091452.png", diff --git a/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md b/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md index 4ef5b68..7ba9afc 100644 --- a/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md +++ b/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md @@ -83,5 +83,8 @@ Guessing the time duration for suspecting a process: *Proof:* Forall i - i ∉ X $\to$ `ev_leader_i(X)` is any ID (and may change in time) -- $i \in X \to$ `ev_leader_i(X)` $= min\left( suspected_{i} \cap X \right)$ where $Π$ denotes the set of all proc. IDs. +- $i \in X \to$ `ev_leader_i(X)` $= min\left(( Π \setminus suspected_{i}) \cap X \right)$ where $Π$ denotes the set of all proc. IDs. +$\Omega_{X}$ is not stronger than ♢P (so, ♢P is strictly stronger) + +The formal proof consists in showing that if $\Omega$ was stronger than ♢P, then consensus would be possible in an asynchronous system with crashes and atomic R/W registers. \ No newline at end of file