From ef7b965409fc6c4b7c56d8a798078f1a304a779a Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Tue, 1 Apr 2025 09:19:49 +0200 Subject: [PATCH] vault backup: 2025-04-01 09:19:49 --- .../notes/10 - Consensus Implementation.md | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/Concurrent Systems/notes/10 - Consensus Implementation.md b/Concurrent Systems/notes/10 - Consensus Implementation.md index f5c7dce..6ae846f 100644 --- a/Concurrent Systems/notes/10 - Consensus Implementation.md +++ b/Concurrent Systems/notes/10 - Consensus Implementation.md @@ -81,3 +81,15 @@ Wait-freedom, Validity and Integrity hold by construction. Agreement: the first that performs test&set receives 0 and decides his proposal; the other one receives 1 and decides the other proposal. +**Thm:** there exists no A wait free that implements binary consensus for atomic R/W registers and test&set objects for 3 processes. + +*Proof:* +The structure is the same as the previous proof. Consider 3 proc.’s p, q and r. +Let C be bivalent and S maximal s.t. S(C) (call it C’) is bivalent: +- p(C’) is 0-val, q(C’) is 1-val and r(C’) is monovalent (for example) + +Let’s assume that: +- at C’ r stops for a long time +- $op_{p}$ and $op_{q}$ are the next operations that p and q issue from C’ by following A + +1. $op_p$ and $op_q$ are both R/W \ No newline at end of file