vault backup: 2025-04-01 08:54:49

Concurrent Systems/notes/10 - Consensus Implementation.md

@@ -32,3 +32,11 @@ If A wait-free implements binary consensus for n processes, then there exists a
 *Proof:*
 ![[Pasted image 20250401083747.png]]
 
+### CN(Atomic R/W registers) = 1
+**Thm:** There exists no wait-free implementation of binary consensus for 2 processes that uses atomic R/W registers.
+
+*Proof:*
+Assume by contradiction A wait-free, with processes p and q.
+
+By the previous result, it has an initial bivalent configuration C
+-  let S be a sequence of operations s.t. C’ = S(C) is maximally bivalent (i.e., p(S(C)) is 0-valent and q(S(C)) is 1-valent, or viceversa)