diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index 347c2a3..9aee8e6 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -34,9 +34,9 @@
               "type": "pdf",
               "state": {
                 "file": "Concurrent Systems/slides/class 3.pdf",
-                "page": 15,
+                "page": 16,
                 "left": -26,
-                "top": 106,
+                "top": 396,
                 "zoom": 0.57541567695962
               },
               "icon": "lucide-file-text",
@@ -218,9 +218,9 @@
   },
   "active": "6edd4157a160e462",
   "lastOpenFiles": [
-    "Pasted image 20250310103703.png",
     "Concurrent Systems/slides/class 3.pdf",
     "Concurrent Systems/notes/3.md",
+    "Pasted image 20250310103703.png",
     "Concurrent Systems/notes/1 - CS Basics.md",
     "Concurrent Systems/notes/1 - CS Basics2.md",
     "Concurrent Systems/notes/2b - Round Robin algorithm.md",
@@ -248,7 +248,6 @@
     "Concurrent Systems/slides/class 1.pdf",
     "Concurrent Systems/notes/images/Pasted image 20250303093116.png",
     "Concurrent Systems/notes/images/Pasted image 20250303100953.png",
-    "Concurrent Systems/notes/images/Pasted image 20250303100721.png",
     "Foundation of data science/notes/1 CV Basics.md",
     "Foundation of data science/notes/7 Autoencoders.md",
     "Foundation of data science/notes/6 PCA.md",
diff --git a/Concurrent Systems/notes/3.md b/Concurrent Systems/notes/3.md
index ef12932..c74568d 100644
--- a/Concurrent Systems/notes/3.md	
+++ b/Concurrent Systems/notes/3.md	
@@ -255,4 +255,18 @@ unlock(i) :=
 ![[Pasted image 20250310103703.png]]
 so by this, the very worst possible case is that my lock experiences that.
 
-It looks like I can experience at most $2n-1$ other critical sections, but it is even better, let's see:
\ No newline at end of file
+It looks like I can experience at most $2n-1$ other critical sections, but it is even better, let's see:
+...
+
+
+#### Improvement of Aravind’s algorithm
+```
+unlock(i) :=
+	∀j≠i.if DATE[j] > DATE[i] then
+		DATE[j] <- DATE[j]-1
+		DATE[i] <- n STAGE[i] <- 0
+		FLAG[i] <- down
+```
+
+Since the LOCK is like before, the revised protocol satisfies MUTEX. Furthermore, you can prove that it satisfies bounded bypass with bound n-1 -> EXERCISE!
+