vault backup: 2025-03-18 15:30:04

.obsidian/community-plugins.json

@@ -5,6 +5,5 @@
   "mathlive-in-editor-mode",
   "smart-second-brain",
   "local-gpt",
-  "obsidian-latex-suite",
   "companion"
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.obsidian/workspace.json

@@ -6,7 +6,6 @@
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@@ -25,17 +24,20 @@
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+        "id": "4ae2dccd2d32173d",
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+            "id": "88f2e3a5b973712d",
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             "state": {
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               "state": {
-                "file": "Concurrent Systems/slides/class 6.pdf"
+                "file": "Concurrent Systems/slides/class 6.pdf",
+                "page": 5,
+                "left": -19,
+                "top": 573,
+                "zoom": 0.7998812351543944
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               "icon": "lucide-file-text",
               "title": "class 6"
@@ -94,12 +96,12 @@
               "title": "Segnalibri"
             }
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+        ]
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+    "width": 307.5,
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@@ -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
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+    "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",

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