vault backup: 2025-03-10 23:08:12

Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md

@@ -94,7 +94,10 @@ lock(i) :=
 -  $p_n$ invokes lock alone, completes its CS and its new DATE is n
 - all other $p_i, i \in P$ (with P being the set of all processes) will have `DATE[i] < n`, as their value for DATE is decreased
 - suppose every process invoke lock, then $p_n$ has to wait all other processes to complete their CSs
-- scenario 1: every process keeps 
+- *scenario 1*: every other $p_i$ keep invoking lock again immediately after the unlock
+	- `DATE[i]` will always be $> DATE[n]$
+	- after $n-1$ turns, `DATE[n]` will have `DATE[n] = 1`, with every other `DATE[i] > 1, i!=n`  -> ️✅
+- *scenario 2*: not every process invokes the lock
 
 **Lemma 1:** Suppose we have $n$ processes, then $\not \exists p_{j} : DATE[j]=DATE[i] \forall i \in [0, n]$ (non esistono due processi con lo stesso valore per DATE)
 *Proof:*