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

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: