vault backup: 2025-03-10 22:33:12

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

@@ -93,6 +93,9 @@ lock(i) :=
 
 -  $p_n$ invokes lock alone, completes its CS and its new DATE is n
 
-**Lemma 1:** DATE's bounds are $[0, n]$
+**Lemma 1:** Suppose we have $n$ processes, then $\not \exists p_{j} : DATE[j]=DATE[i] \forall i \in [0, n]$
+
+**Lemma 2:** DATE's bounds are $[0, n]$
 *Proof:*
-For the upper bound, it's trivial: DATE is either decreased or set to $n$.
+For the upper bound, it's trivial: DATE is either decreased or set to $n$.
+...