From 9219ace7c8bc79be6190575aa34818c06b3404b0 Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Tue, 1 Apr 2025 08:39:49 +0200 Subject: [PATCH] vault backup: 2025-04-01 08:39:49 --- .obsidian/workspace.json | 1 + .../notes/10 - Consensus Implementation.md | 9 ++++++++- Pasted image 20250401083747.png | Bin 0 -> 159471 bytes 3 files changed, 9 insertions(+), 1 deletion(-) create mode 100644 Pasted image 20250401083747.png diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 8d0d4b5..533f0ca 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -213,6 +213,7 @@ }, "active": "483215723737b6f7", "lastOpenFiles": [ + "Pasted image 20250401083747.png", "Concurrent Systems/slides/class 10.pdf", "Concurrent Systems/notes/10 - Consensus Implementation.md", "Concurrent Systems/notes/3a - Hardware primitives & Lamport Bakery algorithm.md", diff --git a/Concurrent Systems/notes/10 - Consensus Implementation.md b/Concurrent Systems/notes/10 - Consensus Implementation.md index 0dea4fb..cef0a9d 100644 --- a/Concurrent Systems/notes/10 - Consensus Implementation.md +++ b/Concurrent Systems/notes/10 - Consensus Implementation.md @@ -24,4 +24,11 @@ Let's consider binary consensus implemented by an algorithm A by using base obje 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 +- **bivalent**, otherwise. + +### Fundamental theorem +If A wait-free implements binary consensus for n processes, then there exists a bivalent initial configuration. + +*Proof:* +![[Pasted image 20250401083747.png]] + diff --git a/Pasted image 20250401083747.png b/Pasted image 20250401083747.png new file mode 100644 index 0000000000000000000000000000000000000000..40c78a182fe9a5a79711699df5c7a4c3360ae3ff GIT binary patch literal 159471 zcmcGVWmFx_)8KCiP6+NA+%N79!QGv}h2Rj}-QC^Y-QC^YA-KEy@_(Lpci-L5yC3HC znVC~vJ=4`aHC6QsmXi^MhsA~k008jfV!{dl0Qflo0A>RX_Ic&i5_A8vf%zk*ZVLc> z@B7d3C7${_4gf$15Em9ua!NZ*htUdKed&rcdu`WV&m?Q6(y~Zc&|KD#57vY!ZZa0A zQQ02pFi1?NK~fk_XrgQm$ulp`Q<#=Hsb`i?$+kZDa86AAUB0}+zA2j-c{Raxz;n=c zzIHBNUJbM8k7v=CYo?(yvy zjQfjKi7ZupF3>si3F)>a_Ek5mI&vycbs!G4nB(`AXZ$Sf&-jIg->Tr)blkwt5M(o- zm6S9jFTBF|TZk;?yXDJwR^AXSI4YElUh!;7#cBlZT^D^m#|$Y1cC6UT$`P)a)OGml 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