From 6b746d3f7ca963524f8efb07aa1c6d5cd0e415c5 Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Tue, 1 Apr 2025 08:34:49 +0200 Subject: [PATCH] vault backup: 2025-04-01 08:34:49 --- .../notes/10 - Consensus Implementation.md | 12 ++++++++++-- 1 file changed, 10 insertions(+), 2 deletions(-) diff --git a/Concurrent Systems/notes/10 - Consensus Implementation.md b/Concurrent Systems/notes/10 - Consensus Implementation.md index 2672b66..0dea4fb 100644 --- a/Concurrent Systems/notes/10 - Consensus Implementation.md +++ b/Concurrent Systems/notes/10 - Consensus Implementation.md @@ -13,7 +13,15 @@ For all T, CN(T) > 0; if there is no sup, we let CN(T) := +∞ - contradiction with CN(T1) < n ### Schedules and Configurations -**Schedule:** sequence of operation invocations issued by processes +**Schedule:** sequence of operation invocations issued by processes. + **Configuration:** the global state of a system at a given execution time (values of the shared memory + local state of every process). -Given a configuration C and a schedule S, we denote with S(C) the configuration obtained starting from C and applying S. \ No newline at end of file +Given a configuration C and a schedule S, we denote with S(C) the configuration obtained starting from C and applying S. + +Let's consider binary consensus implemented by an algorithm A by using base objects and atomic R/W registers; let us call $S_A$ a schedule induced by A. + +A configuration C obtained during the execution of all A is called: +- **v-valent** if $S_A(C)$ decides v, for every $S_A$ +- **monovalent**, if there exists $v \in \{0,1\}$ s.t. C is v-valent +- **bivalent**, otherwise. \ No newline at end of file