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Concurrent Systems/notes/7- MUTEX-free concurrency.md

@@ -21,5 +21,35 @@ We have four new liveness properties
 ### A wait-free Splitter
 Assume we have atomic R/W registers.
 
-A **splitter** is a concurrent object that provides a single operation dir such that:
-1. (*validity*) 
+A **splitter** is a concurrent object that provides a single operation **dir** such that:
+1. (*validity*) it returns L, R or S (left, right, stop)
+2. (*concurrency*) in case of n simultaneous invocations of **dir**
+	1. at most n-1 L are returned
+	2. at most n-1 R are returned
+	3. at most 1 S is returned
+3. (*wait freedom*) it eventually terminates.
+
+Idea:
+- not all processes obtain the same value
+- in a solo execution (i.e., without concurrency) the invoking process must stop (0 L && 0 R && at most 1 S)
+
+We have:
+- DOOR: MRMW boolean atomic register initialized at 1
+- LAST: MRMW atomic register initialized at whatever process index
+
+```
+dir(i) :=
+	LAST <- i
+	if DOOR = 0 then
+		retunr R
+	else
+		DOOR <- 0
+	if LAST = i then
+		return S
+	else
+		return L
+```
+With 2 processes, we can have:
+- one goes left and one goes right
+- one goes left and the other stops
+- one goes right and the other stops