vault backup: 2025-03-25 09:23:01

.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",

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.