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

@@ -8,4 +8,24 @@ Can we take the most basic protocol that satisfies the most basic liveness prope
 
 **Why is it different from lock/unlock?** Because this allows failures, and they can also happen in the contention-free period.
 
-PROBLEM: to distinguish a failure from a long delay, we need objects called ***failure detectors***, that provide processes information on the failed processes of the system. According to the type/quality of the info, several F.
+**PROBLEM:** to distinguish a failure from a long delay, we need objects called ***failure detectors***, that provide processes information on the failed processes of the system. According to the type/quality of the info, several F.D.s can be defined.
+
+**Eventually restricted leadership:** given a non-empty set of process IDs X, the failure detector $\Omega_{X}$ provides each process a local variable `ev_leader(X)` such that:
+1. *(Validity)* `ev_leader(x)` always contains a process ID
+2. *(Eventual leadership)* eventually, all `ev_leader(X)` of all non-crashed processes of X for ever contain the same process ID, that is one of them
+
+REMARK: the moment in which all variables contain the same leader is unknown
+
+```
+REMARK: the moment in which all variables contain the same leader is unknown
+
+need_help(i) :=
+	NEED_HELP[i] <- true
+	repeat
+		X <- {j : NEED_HELP[j]}
+	until ev_leader(X) = i
+
+stop_help(i) :=
+	NEED_HELP[i] <- false
+```
+