vault backup: 2025-03-10 23:28:03

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

@@ -91,11 +91,11 @@ lock(i) :=
 	until foreach j != i, STAGE[j] = 0
 ```
 
--  $p_n$ 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
+-  $p_n$ invokes lock alone, completes its CS and so `DATE[n] = n`
+- then as DATE is either set to n or decreased, for each i, `DATE[i] < n`
 - *scenario 1*: every other $p_i$ keep invoking lock again immediately after the unlock
 	- every time some process exits the CS, `DATE[n]` is decreased
 	- 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
 	- eventually, more than one process will have its DATE set to 0
-	- but there will still be at most $n-1$ processes $p_i$ with `DATE[i] < DATE[n]`, this ensures that after $n-1$ -> ✅
+	- but there will still be at most $n-1$ processes $p_i$ with `DATE[i] < DATE[n]`, this ensures that after $n-1$ steps, every other process $p_i$ will have `DATE[i] > DATE[n]` -> ✅