From d3b9c563dc2045617f0da09edb9abc41363906bf Mon Sep 17 00:00:00 2001
From: Marco Realacci <realacci.1938880@gamlab11.gamlab.sapienzaapps.it>
Date: Tue, 18 Mar 2025 15:30:04 +0100
Subject: [PATCH] vault backup: 2025-03-18 15:30:04

---
 .obsidian/community-plugins.json              |   1 -
 .obsidian/workspace.json                      |  34 +++++++++++-------
 Concurrent Systems/notes/6 - Atomicity.md     |   6 +++-
 .../images/Pasted image 20250318090733.png    | Bin
 .../images/Pasted image 20250318090909.png    | Bin
 5 files changed, 26 insertions(+), 15 deletions(-)
 rename Pasted image 20250318090733.png => Concurrent Systems/notes/images/Pasted image 20250318090733.png (100%)
 rename Pasted image 20250318090909.png => Concurrent Systems/notes/images/Pasted image 20250318090909.png (100%)

diff --git a/.obsidian/community-plugins.json b/.obsidian/community-plugins.json
index 49ffe43..0871a1f 100644
--- a/.obsidian/community-plugins.json
+++ b/.obsidian/community-plugins.json
@@ -5,6 +5,5 @@
   "mathlive-in-editor-mode",
   "smart-second-brain",
   "local-gpt",
-  "obsidian-latex-suite",
   "companion"
 ]
\ No newline at end of file
diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index ec77d71..2ab0866 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -6,7 +6,6 @@
       {
         "id": "4c1f5b7a6abb1339",
         "type": "tabs",
-        "dimension": 44.41260744985673,
         "children": [
           {
             "id": "51157f32453cba69",
@@ -25,17 +24,20 @@
         ]
       },
       {
-        "id": "e12a3c14771a10e5",
+        "id": "4ae2dccd2d32173d",
         "type": "tabs",
-        "dimension": 55.58739255014327,
         "children": [
           {
-            "id": "f04931d588bd12d2",
+            "id": "88f2e3a5b973712d",
             "type": "leaf",
             "state": {
               "type": "pdf",
               "state": {
-                "file": "Concurrent Systems/slides/class 6.pdf"
+                "file": "Concurrent Systems/slides/class 6.pdf",
+                "page": 5,
+                "left": -19,
+                "top": 573,
+                "zoom": 0.7998812351543944
               },
               "icon": "lucide-file-text",
               "title": "class 6"
@@ -94,12 +96,12 @@
               "title": "Segnalibri"
             }
           }
-        ],
-        "currentTab": 1
+        ]
       }
     ],
     "direction": "horizontal",
-    "width": 307.5
+    "width": 307.5,
+    "collapsed": true
   },
   "right": {
     "id": "bc4b945ded1926e3",
@@ -204,15 +206,21 @@
       "canvas:Create new canvas": false,
       "daily-notes:Open today's daily note": false,
       "templates:Insert template": false,
-      "command-palette:Open command palette": false
+      "command-palette:Open command palette": false,
+      "obsidian-ocr:Search OCR": false,
+      "pdf-plus:PDF++: Toggle auto-copy": false,
+      "pdf-plus:PDF++: Toggle auto-focus": false,
+      "pdf-plus:PDF++: Toggle auto-paste": false,
+      "obsidian-git:Open Git source control": false,
+      "companion:Toggle completion": false
     }
   },
-  "active": "51157f32453cba69",
+  "active": "88f2e3a5b973712d",
   "lastOpenFiles": [
-    "Concurrent Systems/slides/class 6.pdf",
     "Concurrent Systems/notes/6 - Atomicity.md",
-    "Pasted image 20250318090909.png",
-    "Pasted image 20250318090733.png",
+    "Concurrent Systems/slides/class 6.pdf",
+    "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/5 - Software Transactional Memory.md",
     "Concurrent Systems/notes/4c - Dining Philosophers.md",
diff --git a/Concurrent Systems/notes/6 - Atomicity.md b/Concurrent Systems/notes/6 - Atomicity.md
index 2677684..3890270 100644
--- a/Concurrent Systems/notes/6 - Atomicity.md	
+++ b/Concurrent Systems/notes/6 - Atomicity.md	
@@ -35,8 +35,12 @@ For all X, let $\hat{S}_{X}$ be a linearization of $\hat{H}_{X}$
 
 Let $\to$ denote $\to_{H} \cup \bigcup_{X \in H} \to _{X}$
 
-We now show that $->$ is acyclic.
+We now show that $\to$ is acyclic.
+1. It cannot have cycles with 1 edge (i.e. self loops): indeed, if $op \to op$, this would mean that $res(op) < inv(op)$, which of course does not make any sense.
 
+2. it cannot have cycles with 2 edges:
+	- let's assume that $op \to op' \to op$
+	- both arrows cannot be $\to_H$ nor $\to_X$ (for some X)
 
 
 > [!PDF|red] class 6, p.6>  we would have a cycle of length 
diff --git a/Pasted image 20250318090733.png b/Concurrent Systems/notes/images/Pasted image 20250318090733.png
similarity index 100%
rename from Pasted image 20250318090733.png
rename to Concurrent Systems/notes/images/Pasted image 20250318090733.png
diff --git a/Pasted image 20250318090909.png b/Concurrent Systems/notes/images/Pasted image 20250318090909.png
similarity index 100%
rename from Pasted image 20250318090909.png
rename to Concurrent Systems/notes/images/Pasted image 20250318090909.png