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Marco Realacci 2025-03-25 09:23:01 +01:00
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5
Concurrent Systems/notes/8 - Enhancing Liveness Properties.md
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@ -83,5 +83,8 @@ Guessing the time duration for suspecting a process:
*Proof:*
Forall i
- i ∉ X $\to$ `ev_leader_i(X)` is any ID (and may change in time)
- $i \in X \to$ `ev_leader_i(X)` $= min\left( suspected_{i} \cap X \right)$ where $Π$ denotes the set of all proc. IDs.
- $i \in X \to$ `ev_leader_i(X)` $= min\left(( Π \setminus suspected_{i}) \cap X \right)$ where $Π$ denotes the set of all proc. IDs.
$\Omega_{X}$ is not stronger than ♢P (so, ♢P is strictly stronger)
The formal proof consists in showing that if $\Omega$ was stronger than ♢P, then consensus would be possible in an asynchronous system with crashes and atomic R/W registers.