From efcd98f2d35caac5160ae2253d40ac52a26ec8dc Mon Sep 17 00:00:00 2001
From: Marco Realacci <realacci.1938880@gamlab11.gamlab.sapienzaapps.it>
Date: Tue, 18 Mar 2025 17:30:04 +0100
Subject: [PATCH] vault backup: 2025-03-18 17:30:04

---
 .obsidian/workspace.json                  | 6 ++++--
 Concurrent Systems/notes/6 - Atomicity.md | 7 ++++---
 2 files changed, 8 insertions(+), 5 deletions(-)

diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index a8644e3..b44ffbb 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -6,6 +6,7 @@
       {
         "id": "4c1f5b7a6abb1339",
         "type": "tabs",
+        "dimension": 50.63775510204081,
         "children": [
           {
             "id": "51157f32453cba69",
@@ -26,6 +27,7 @@
       {
         "id": "4ae2dccd2d32173d",
         "type": "tabs",
+        "dimension": 49.36224489795919,
         "children": [
           {
             "id": "88f2e3a5b973712d",
@@ -36,8 +38,8 @@
                 "file": "Concurrent Systems/slides/class 6.pdf",
                 "page": 6,
                 "left": -23,
-                "top": 379,
-                "zoom": 0.6627078384798101
+                "top": 584,
+                "zoom": 0.6538004750593824
               },
               "icon": "lucide-file-text",
               "title": "class 6"
diff --git a/Concurrent Systems/notes/6 - Atomicity.md b/Concurrent Systems/notes/6 - Atomicity.md
index 7695939..24c0ed6 100644
--- a/Concurrent Systems/notes/6 - Atomicity.md	
+++ b/Concurrent Systems/notes/6 - Atomicity.md	
@@ -69,15 +69,16 @@ This said, we can say that **every DAG admits a topological order** (a total ord
 Let us define a linearization of $\hat{H}$ as follows: $$\hat{S}=inv(op1)res(op1)inv(op2)res(op2)...$$
 we would have the topological order: $op1\to'op2\to'...$
 
-$\to'_X$
+$\to'|_X$
 $\to|_X$
 $\to_X$
 
-Si ha che $\to|_X \space \subseteq \space \to'_X$ perché l'ordinamento topologico è letteralmente la sequenza di eventi in $\hat{S}$
+Osservazione: $\to'|_X$ è come dire $\to_{\hat{S}|X}$, infatti l'ordinamento topologico 
+Si ha che $\to|_X \space \subseteq \space \to'|_X$ perché l'ordinamento topologico è letteralmente la sequenza di eventi in $\hat{S}$
 
 $\hat{S}$ is clearly sequential. Moreover:
 1. $\forall X :\hat{S}|_{X} = \hat{S}_X (\in semantics(X))$, indeed:
-	- $<_{\hat{S}_X} \space = \space\to_X\space \subseteq\space \space\to|_X\space \subseteq\space \to'_X\space = \space\to_{\hat{S}|X}\space=\space<_{\hat{S}|X}$
+	- $<_{\hat{S}_X} \space = \space\to_X\space \subseteq\space \space\to|_X\space \subseteq\space \to'|_X\space = \space\to_{\hat{S}|X}\space=\space<_{\hat{S}|X}$
 		- commento per non diventare scemi:
 			- $\hat{S}_X$ lo storico ottenuto linearizzando $\hat{H}|_X$ 
 				- definisce una relazione di ordinamento $\to_X$