From 10447c9ab994f208f7e739262519222c6474119d Mon Sep 17 00:00:00 2001
From: Marco Realacci <marco@marcorealacci.me>
Date: Tue, 25 Mar 2025 17:12:22 +0100
Subject: [PATCH] vault backup: 2025-03-25 17:12:22

---
 .obsidian/workspace.json                                  | 8 ++++----
 .../notes/8 - Enhancing Liveness Properties.md            | 5 +++--
 2 files changed, 7 insertions(+), 6 deletions(-)

diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index edfd9a0..d0e5832 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -6,7 +6,7 @@
       {
         "id": "efd2410a71337f52",
         "type": "tabs",
-        "dimension": 64.46991404011462,
+        "dimension": 53.86819484240688,
         "children": [
           {
             "id": "383fb8ddbc7a9dc8",
@@ -42,7 +42,7 @@
       {
         "id": "496ffcebad48669d",
         "type": "tabs",
-        "dimension": 35.53008595988539,
+        "dimension": 46.13180515759313,
         "children": [
           {
             "id": "879210c00db77468",
@@ -229,9 +229,9 @@
   },
   "active": "0d64f519fd7f9420",
   "lastOpenFiles": [
-    "Concurrent Systems/notes/7- MUTEX-free concurrency.md",
-    "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/slides/class 7.pdf",
     "Concurrent Systems/notes/6a - Alternatives to Atomicity.md",
     "Concurrent Systems/notes/3a - Hardware primitives & Lamport Bakery algorithm.md",
diff --git a/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md b/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md
index b34e53c..8382670 100644
--- a/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md	
+++ b/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md	
@@ -95,12 +95,13 @@ Forall i
 $\Omega_{X}$ is not stronger than ♢P (so, ♢P is strictly stronger)
 
 The formal proof consists in showing that if $\Omega_{X}$ was stronger than ♢P, then consensus would be possible in an asynchronous system with crashes and atomic R/W registers.
-(because ♢P can solve consensus, )
+(because ♢P can be used to solve consensus)
 #### A contention manager for ♢P
 We assume a weak timestamp generator, i.e. a function such that, if it returns a positive value t to some process, only a finite number of invocations can obtain a timestamp smaller than or equal to t
 
 ```
 TS[1..n] : SWMR atomic R/W registers init at 0
 
-...
+need_help(i) :=
+	TS[i]
 ```
\ No newline at end of file