vault backup: 2025-04-01 09:19:49

Concurrent Systems/notes/10 - Consensus Implementation.md

@@ -81,3 +81,15 @@ Wait-freedom, Validity and Integrity hold by construction.
 
 Agreement: the first that performs test&set receives 0 and decides his proposal; the other one receives 1 and decides the other proposal.
 
+**Thm:** there exists no A wait free that implements binary consensus for atomic R/W registers and test&set objects for 3 processes.
+
+*Proof:*
+The structure is the same as the previous proof. Consider 3 proc.’s p, q and r.
+Let C be bivalent and S maximal s.t. S(C) (call it C’) is bivalent:
+- p(C’) is 0-val, q(C’) is 1-val and r(C’) is monovalent (for example)
+
+Let’s assume that:
+- at C’ r stops for a long time
+- $op_{p}$ and $op_{q}$ are the next operations that p and q issue from C’ by following A
+
+1. $op_p$ and $op_q$ are both R/W