vault backup: 2025-03-04 12:40:54

Concurrent Systems/notes/Lezione2.md

@@ -36,11 +36,15 @@ lock(i) :=
 		wait Y = ⊥
 		goto *
 	else Y <- i
+	
 	if X = i then return
 	else FLAG[i] <- down
+	
 	∀j.wait FLAG[j] = down
+	
 	if Y = i then return
 	else wait Y = ⊥
+	
 	goto *
 
 unlock(i) :=
@@ -49,15 +53,13 @@ unlock(i) :=
 	return
 ```
 
-MUTEX proof
-
+##### MUTEX proof
 How can pi enter its CS?
 ![[Pasted image 20250304084537.png]]
 
 ![[Pasted image 20250304084901.png]]
 
-Deadlock freedom
-
+##### Deadlock freedom
 Let $p_i$ invoke lock
 - If it eventually wins -> √
 - If it is blocked forever, where can it be blocked?
@@ -73,7 +75,8 @@ Let $p_i$ invoke lock
 	- 3. In the first wait Y = ⊥
 		- since pj read a value different from ⊥, there is at least one pk that wrote Y before (but has not yet unlocked)
 		- if $p_k$ eventually enters its CS -> ok, otherwise it must be blocked forever as well. Where?
-			- ![[Pasted image 20250304090207.png]]
+			- In the second wait Y = ⊥: but then there exists a $p_h$ that eventually enters its CS -> good
+			- In the ∀j.wait FLAG[j]=down: this wait cannot block a process forever
 
 ![[Pasted image 20250304090219.png]]