vault backup: 2025-04-01 08:39:49

.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",

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.
+- **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]]
+