From 5359a791f66f9bf512db5bc43792f326a9cdd8c6 Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Tue, 25 Mar 2025 16:27:22 +0100 Subject: [PATCH] vault backup: 2025-03-25 16:27:22 --- Concurrent Systems/notes/8 - Enhancing Liveness Properties.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md b/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md index f79eb8c..faf3a39 100644 --- a/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md +++ b/Concurrent Systems/notes/8 - Enhancing Liveness Properties.md @@ -57,7 +57,7 @@ It can be proved that there exists no wait-free implementation of $\Omega$ in an 1. $\exists$ time $\tau_{1}$, time interval $\nabla$ and correct process $p_{L}$ s.t. after $\tau_{1}$ every two consecutive writes to a specific SWMR atomic R/W by $p_{L}$ are at most $\nabla$ time units apart one from the other 2. let t be an upper bound on the number of possible failing processes and f the real number of process failed (hence, $0\leq f\leq t\leq n-1$, with f unknown and t known in advance). - Then, there are at least $t-f$ correct processes different from $p_L$ with a timer s.t. $\exists$ time $\tau_{2} \forall$ time interval $\delta$, if their timer is set to $\delta$ after $\tau_{2}$, it expires at least after $\delta$. + Then, there are at least $t-f$ correct processes different from $p_L$ with a timer s.t. $\exists$ time $\tau_{2}$ for each time interval $\delta$, if their timer is set to $\delta$ after $\tau_{2}$, it expires at least after $\delta$. REMARK: $\tau_{1}, \tau_{2}, \nabla$ and $p_L$ are all unknown.