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Marco Realacci 2025-03-10 23:18:12 +01:00
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Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md
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@ -93,13 +93,12 @@ lock(i) :=
- $p_n$ invokes lock alone, completes its CS and its new DATE is n - $p_n$ 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 - 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 other $p_i$ keep invoking lock again immediately after the unlock - *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 - 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` -> ️✅ - 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 - *scenario 2*: not every process invokes the lock
- eventually, - eventually, more than one process will have its DATE set to 0
- there will be at most $n-1$ processes $p_i$ with `DATE[i] < DATE[n]` -> ✅