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Marco Realacci 2025-03-31 09:15:43 +02:00
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35
Concurrent Systems/notes/9 - Consensus.md
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@ -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: 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 <- ⊥ result_i <- ⊥
invoc_i <- ⟨op(args) , i⟩ invoc_i <- ⟨op(args) , i⟩
wait result_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 The local simulation of Z by $p_i$ is
``` ```
on the background thread of pi:
k <- 0 k <- 0
z_i <- Z.init() z_i <- Z.init()
while true while true
@ -72,13 +76,12 @@ while true
``` ```
This solution is non-blocking but not wait-free (can run forever). This solution is non-blocking but not wait-free (can run forever).
P.S. *invoc_i*, *result_i* e *z_i* sono variabili locali. P.S. *invoc_i*, *result_i* e *z_i* sono variabili locali.
### A wait-free construction ### A wait-free construction
- `LAST_OP[1..n]:` array of SWMR atomic R/W registers containing pairs init at ⟨⊥,0⟩ ∀i - `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 - 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 - `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 - 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. 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 != ⊥ wait result_i != ⊥
return 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 local simulation of Z by p_i
k <- 0 k <- 0
z_i <- Z.init() z_i <- Z.init()
while true while true
invoc_i <- 𝜀 invoc_i <- 𝜀
∀ j = 1..n ∀ j = 1..n
if 𝜋2(LAST_OP[j])>last_sni[j] then if 𝜋2(LAST_OP[j]) > last_sn_i[j] then
invoci.append( ⟨𝜋1(LAST_OP[j]),j⟩ ) # j ha fatto una nuova proposta
if invoci ≠ 𝜀 then invoc_i.append(⟨𝜋1(LAST_OP[j]),j⟩)
k++ # allora la aggiungo alla mia lista invoc_i
exec_i <- CONS[k].propose(invoci) if invoci ≠ 𝜀 then
for r=1 to |execi| k++
⟨zi,res⟩ -> 𝛿(zi,𝜋1(execi[r])) exec_i <- CONS[k].propose(invoci)
j <- 𝜋2(execi[r]) for r=1 to |execi|
last_sni[j]++ ⟨zi,res⟩ -> 𝛿(zi,𝜋1(execi[r]))
if i=j then j <- 𝜋2(execi[r])
result_i <- res last_sni[j]++
if i=j then
result_i <- res
``` ```
As before, they are executed by each process on two threads.