From 051b47564b829fde2530d47623d27df315f5a17c Mon Sep 17 00:00:00 2001
From: Marco Realacci <marco@marcorealacci.me>
Date: Mon, 31 Mar 2025 09:15:43 +0200
Subject: [PATCH] vault backup: 2025-03-31 09:15:43

---
 Concurrent Systems/notes/9 - Consensus.md | 35 ++++++++++++++---------
 1 file changed, 22 insertions(+), 13 deletions(-)

diff --git a/Concurrent Systems/notes/9 - Consensus.md b/Concurrent Systems/notes/9 - Consensus.md
index 42a8f09..9f1e85a 100644
--- a/Concurrent Systems/notes/9 - Consensus.md	
+++ b/Concurrent Systems/notes/9 - Consensus.md	
@@ -43,6 +43,8 @@ Let us first concentrate on obj's with deterministic specifications (we will see
 
 A process $p_i$ that wants to invoke operation op of object Z with arguments args locally runs:
 ```
+on the foreground thread of pi:
+
 result_i <- ⊥
 invoc_i <- ⟨op(args) , i⟩
 wait result_i != ⊥
@@ -59,6 +61,8 @@ Let CONS be an unbounded array of consensus objects and 𝜋1 and 𝜋2 respecti
 The local simulation of Z by $p_i$ is
 
 ```
+on the background thread of pi:
+
 k <- 0
 z_i <- Z.init()
 while true
@@ -72,13 +76,12 @@ while true
 ```
 This solution is non-blocking but not wait-free (can run forever).
 P.S. *invoc_i*, *result_i* e *z_i* sono variabili locali.
-
 ### A wait-free construction
 - `LAST_OP[1..n]:` array of SWMR atomic R/W registers containing pairs init at ⟨⊥,0⟩ ∀i
 	- è condiviso e ogni processo ci infila le sue proposal
 - `last_sn_i[1..n]:` local array of the last op by $p_j$ executed by $p_i$ init at 0 ∀i,j
 	- ogni processo ha la sua copia locale
-	- `last_sn_i[j]` traccia dell'ultima operazione eseguita da j
+	- `last_sn_i[j]` tiene traccia dell'ultima operazione eseguita da j
 
 Idea: instead of just proposing my proposal, at every moment I propose all the proposals of all the processes.
 
@@ -89,21 +92,27 @@ or(arg) by p_i on Z
 	wait result_i != ⊥
 	return result_i
 
+l'idea è che scrivo la mia proposal sulla shared memory, così ogni processo può leggere la mia proposal.
+
 local simulation of Z by p_i
 	k <- 0
 	z_i <- Z.init()
 	while true
 		invoc_i <- 𝜀
 		∀ j = 1..n
-			if 𝜋2(LAST_OP[j])>last_sni[j] then
-			invoci.append( ⟨𝜋1(LAST_OP[j]),j⟩ )
-			if invoci ≠ 𝜀 then
-				k++
-				exec_i <- CONS[k].propose(invoci)
-				for r=1 to |execi|
-					⟨zi,res⟩ -> 𝛿(zi,𝜋1(execi[r]))
-					j <- 𝜋2(execi[r])
-					last_sni[j]++
-					if i=j then 
-						result_i <- res
+			if 𝜋2(LAST_OP[j]) > last_sn_i[j] then
+				# j ha fatto una nuova proposta
+				invoc_i.append(⟨𝜋1(LAST_OP[j]),j⟩)
+				# allora la aggiungo alla mia lista invoc_i
+				if invoci ≠ 𝜀 then
+					k++
+					exec_i <- CONS[k].propose(invoci)
+					for r=1 to |execi|
+						⟨zi,res⟩ -> 𝛿(zi,𝜋1(execi[r]))
+						j <- 𝜋2(execi[r])
+						last_sni[j]++
+						if i=j then 
+							result_i <- res
 ```
+As before, they are executed by each process on two threads.
+