vault backup: 2025-03-10 10:40:13

.obsidian/workspace.json

@@ -34,9 +34,9 @@
               "type": "pdf",
               "state": {
                 "file": "Concurrent Systems/slides/class 3.pdf",
-                "page": 14,
+                "page": 15,
                 "left": -26,
-                "top": 41,
+                "top": 106,
                 "zoom": 0.57541567695962
               },
               "icon": "lucide-file-text",
@@ -218,6 +218,7 @@
   },
   "active": "6edd4157a160e462",
   "lastOpenFiles": [
+    "Pasted image 20250310103703.png",
     "Concurrent Systems/slides/class 3.pdf",
     "Concurrent Systems/notes/3.md",
     "Concurrent Systems/notes/1 - CS Basics.md",

Concurrent Systems/notes/3.md

@@ -246,4 +246,13 @@ unlock(i) :=
 	- Otherwise let $p_j$ be the process that enters, its next date is $n+1 > DATE[i]$
 		- $p_{j}$ cannot surpass $p_i$ again (before a RESET)
 	- The worst case is then all processes perform lock together and $i = n$ (i am process n)
-		- all $p_{1}\dots p_{n}$ surpass $
+		- all $p_{1}\dots p_{n}$ surpass $p_{n}$
+		- then $p_n$ enters and it resets the DATE in its unlock
+			- only 1 reset and it is the worst case!
+
+**Theorem:** the algorithm satisfies bounded bypass with bound $2n-2$.
+*Proof:*
+![[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: