vault backup: 2025-03-25 09:13:01

Concurrent Systems/notes/8 - Enhancing Liveness Properties.md

@@ -16,6 +16,8 @@ Can we take the most basic protocol that satisfies the most basic liveness prope
 
 REMARK: the moment in which all variables contain the same leader is unknown
 
+#### From obstruction-freedom to non-blocking
+
 ```
 NEED_HELP[1..n] : SWMR atomic R/W boolean registers init at false
 
@@ -57,4 +59,20 @@ It can be proved that there exists no wait-free implementation of $\Omega$ in an
 
 REMARK: $\tau_{1}, \tau_{2}, \nabla$ and $p_L$ are all unknown.
 
-![[Pasted image 20250325090735.png]]
+IDEA:
+- `PROGRESS[1..n]` is an array of SWMR atomic registers used by proc’s to signal that they’re alive
+- pi suspects pj if pi doesn’t see any progress of pj after a proper time interval (to be guessed) set in its timer
+- the leader is the least suspected process, or the one with smallest/biggest ID among the least suspected ones (if there are more than one)
+	- this changes in time, but not forever
+
+Guessing the time duration for suspecting a process:
+- SUSPECT[i,j] = #times pi has suspected pj
+- For all k, take the t+1 minimum values in SUSPECT[1..n , k]
+- Sum them, to obtain Sk
+- The interval to use in the timers is the minimum Sk
+	- it can be proved that this eventually becomes ≥ $\nabla$
+
+#### From obstruction-freedom to wait-freedom
+**Eventually perfect:** failure detector ♢P provides each process $p_i$ a local variable $suspected_i$ such that
+1. *(Eventual completeness)* eventually, $suspended_{i}$ contains all the indexes of crashed processes, for all correct $p_i$
+2. (*Eventual accuracy*)