vault backup: 2025-03-10 17:30:21

Concurrent Systems/notes/3.md

@@ -232,6 +232,7 @@ unlock(i) :=
 Let's consider the execution of $p_i$ leading to its CS:
 ![[Pasted image 20250310172134.png]]
 
+**Corollary** (of the MUTEX proof)**:** DATE is never written concurrently.
 
 #### Bounded bypass proof
 **Lemma 1:** exactly after n CSs there is a reset of DATE.
@@ -246,7 +247,7 @@ Let's consider the execution of $p_i$ leading to its CS:
 - let $p_i$ invoke lock, if no reset occurs, ok
 - otherwise, let us consider the moment in which a reset occurs
 	- if pi is the next process that enters the CS, ok
-	- Otherwise let $p_j$ be the process that enters, its next date is $n+1 > DATE[i]$
+	- 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 $p_{n}$