vault backup: 2025-03-25 08:53:01

.obsidian/workspace.json

@@ -229,10 +229,10 @@
       "companion:Toggle completion": false
     }
   },
-  "active": "879210c00db77468",
+  "active": "0d64f519fd7f9420",
   "lastOpenFiles": [
-    "Concurrent Systems/notes/8 - Enhancing Liveness Properties.md",
     "Concurrent Systems/slides/class 8.pdf",
+    "Concurrent Systems/notes/8 - Enhancing Liveness Properties.md",
     "Concurrent Systems/notes/7- MUTEX-free concurrency.md",
     "Concurrent Systems/notes/images/Pasted image 20250324091452.png",
     "Concurrent Systems/slides/class 7.pdf",

Concurrent Systems/notes/8 - Enhancing Liveness Properties.md

@@ -29,3 +29,13 @@ stop_help(i) :=
 	NEED_HELP[i] <- false
 ```
 
+**Theorem:** the contention manager just seen transforms an obstr.-free implementation into a non-blocking enriched implementation.
+
+*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 ($\forall j \not \in Q$)
+	- $\exists \tau' \geq \tau$ where all proc.'s in Q compute the same X
+
+**Observation:**