vault backup: 2025-03-04 08:29:45

.obsidian/workspace.json

@@ -36,9 +36,9 @@
               "type": "pdf",
               "state": {
                 "file": "Concurrent Systems/slides/class 2.pdf",
-                "page": 1,
+                "page": 2,
                 "left": -23,
-                "top": 72,
+                "top": 542,
                 "zoom": 0.6796318289786224
               },
               "icon": "lucide-file-text",
@@ -220,6 +220,7 @@
   },
   "active": "802d9ec58484849d",
   "lastOpenFiles": [
+    "Pasted image 20250304082459.png",
     "Concurrent Systems/slides/class 2.pdf",
     "Concurrent Systems/notes/Lezione2.md",
     "Concurrent Systems/notes/Lezione1.md",

Concurrent Systems/notes/Lezione2.md

@@ -0,0 +1,21 @@
+Peterson's algorithm cost $O(n^2)$
+A first way to reduce this cost is by using a tournament of MUTEX between pairs of processes:
+![[Pasted image 20250304082459.png|350]]
+
+Of course this is a binary tree, and the height of a binary tree is logaritmic to the number of leaves. A process then wins after $\lceil \log_{2}n \rceil$ competitions $\to O(\log n)$ cost.
+
+But we can do better. Let's see an idea of a constant-time algorithm.
+
+```
+Initialize Y at ⊥, X at any value (e.g., 0)
+
+lock(i) :=
+	x <- i
+	if Y != ⊥ then FAIL
+	else Y <- i
+	if X = i then return
+	else fail
+
+ unlock(i) :=
+	 Y <- ⊥
+	 return