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Marco Realacci 2025-04-01 08:39:49 +02:00
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.obsidian/workspace.json vendored
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@ -213,6 +213,7 @@
}, },
"active": "483215723737b6f7", "active": "483215723737b6f7",
"lastOpenFiles": [ "lastOpenFiles": [
"Pasted image 20250401083747.png",
"Concurrent Systems/slides/class 10.pdf", "Concurrent Systems/slides/class 10.pdf",
"Concurrent Systems/notes/10 - Consensus Implementation.md", "Concurrent Systems/notes/10 - Consensus Implementation.md",
"Concurrent Systems/notes/3a - Hardware primitives & Lamport Bakery algorithm.md", "Concurrent Systems/notes/3a - Hardware primitives & Lamport Bakery algorithm.md",

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Concurrent Systems/notes/10 - Consensus Implementation.md
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@ -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: A configuration C obtained during the execution of all A is called:
- **v-valent** if $S_A(C)$ decides v, for every $S_A$ - **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 - **monovalent**, if there exists $v \in \{0,1\}$ s.t. C is v-valent
- **bivalent**, otherwise. - **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]]

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