vault backup: 2025-03-04 09:34:45

.obsidian/workspace.json

@@ -36,9 +36,9 @@
               "type": "pdf",
               "state": {
                 "file": "Concurrent Systems/slides/class 2.pdf",
-                "page": 8,
+                "page": 13,
                 "left": -23,
-                "top": 74,
+                "top": 266,
                 "zoom": 0.6796318289786224
               },
               "icon": "lucide-file-text",
@@ -220,6 +220,7 @@
   },
   "active": "802d9ec58484849d",
   "lastOpenFiles": [
+    "Pasted image 20250304093223.png",
     "Pasted image 20250304090219.png",
     "Pasted image 20250304090207.png",
     "Pasted image 20250304084901.png",
@@ -265,7 +266,6 @@
     "Biometric Systems/notes/8 Face anti spoofing.md",
     "Biometric Systems/notes/1. Introduction.md",
     "Biometric Systems/images/Pasted image 20241228171617.png",
-    "Biometric Systems/images/Pasted image 20241228174722.png",
     "Senza nome.canvas"
   ]
 }

Concurrent Systems/notes/Lezione2.md

@@ -121,4 +121,14 @@ Let Y be the set of processes competing for the CS (suspended on the DLF.lock)
 	- otherwise, Y shrinks by one. And because of Observation 1, TURN and FLAG[TURN] don't change, so $p_y$ cannot enter Y again.
 - Iterating this reasoning we can see that $p_i$ will eventually win, and the worst case is when is the last winner.
 
-**Lemma 2:** If FLAG[i] = up, then TURN is set to i in at most $(n-1)^2$ 
+**Lemma 2:** If FLAG[i] = up, then TURN is set to i in at most $(n-1)^2$ iterations.
+
+If TURN=i when FLAG[i] is set, done
+By Deadlock freedom of RR, at least one process eventually unlocks
+- If FLAG[TURN] = down, then TURN is increased. Otherwise, by Lemam 1, $p_{TURN}$ wins in at most n-1 iterations and increases TURN.
+- If now TURN = i then we are done. Otherwise, we repeat this reasoning.
+
+The worst case is when TURN = *i+1* mod n when FLAG[i] is set.
+
+![[Pasted image 20250304093223.png]]
+