vault backup: 2025-03-10 09:35:11

.obsidian/workspace.json

@@ -34,10 +34,10 @@
               "type": "pdf",
               "state": {
                 "file": "Concurrent Systems/slides/class 3.pdf",
-                "page": 8,
-                "left": -36,
-                "top": 151,
-                "zoom": 0.4382422802850356
+                "page": 7,
+                "left": -26,
+                "top": 213,
+                "zoom": 0.57541567695962
               },
               "icon": "lucide-file-text",
               "title": "class 3"
@@ -100,7 +100,8 @@
       }
     ],
     "direction": "horizontal",
-    "width": 307.5
+    "width": 307.5,
+    "collapsed": true
   },
   "right": {
     "id": "bc4b945ded1926e3",

Concurrent Systems/notes/3.md

@@ -146,4 +146,12 @@ Se il ticket number è minore si ottiene l'accesso, se il ticket number è ugual
 
 > It is possible that while reading, other processes are writing their turn! So it's possible that I read something unpredictable! We need to consider it in the proofs.
 
-Why is the flag needed? Without it, if two process $i$ and $j$ sets my_turn at the same time, t
+###### Why is the flag needed?
+Without it, if two process $i$ and $j$ sets MY_TURN at the same time, then $i$ goes to sleep, $j$ enters the CS, but when $i$ wakes up, it will enter too!
+
+#### MUTEX proof
+**Lemma 1:** if $p_i$ enters the bakery before $p_j$, then `MY_TURN[i] < MY_TURN[j]`.
+
+*Proof:*
+- let t be the value of `MY_TURN[i]` after $p_{i}$ exits the doorway (after flag <- down)
+- when $p_j$ computes its ticket, it reads $t$ from `MY_TURN[i]`, it reads t from MY_TURNpi