vault backup: 2025-03-18 17:25:04

.obsidian/workspace.json

@@ -214,10 +214,10 @@
       "companion:Toggle completion": false
     }
   },
-  "active": "88f2e3a5b973712d",
+  "active": "51157f32453cba69",
   "lastOpenFiles": [
-    "Concurrent Systems/notes/6 - Atomicity.md",
     "Concurrent Systems/slides/class 6.pdf",
+    "Concurrent Systems/notes/6 - Atomicity.md",
     "Concurrent Systems/notes/images/Pasted image 20250318090733.png",
     "Concurrent Systems/notes/images/Pasted image 20250318090909.png",
     "Concurrent Systems/slides/class 5.pdf",

Concurrent Systems/notes/6 - Atomicity.md

@@ -69,9 +69,15 @@ 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: $op1\to'op2\to'...$
 
+$\to'_X$
+$\to|_X$
+$\to_X$
+
+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:
-	- $<_{\hat{S}_X} \space = \space\to_X\space \subseteq\space \to'_X\space = \space\to_{\hat{S}|X}\space=\space<_{\hat{S}|X}$
+	- $<_{\hat{S}_X} \space = \space\to_X\space \subseteq\space \space\to|_X\space \subseteq\space \to'_X\space = \space\to_{\hat{S}|X}\space=\space<_{\hat{S}|X}$
 		- commento per non diventare scemi:
 			- $\hat{S}_X$ lo storico ottenuto linearizzando $\hat{H}|_X$ 
 				- definisce una relazione di ordinamento $\to_X$