vault backup: 2025-03-03 09:42:47

Concurrent Systems/notes/Lezione1.md

@@ -108,7 +108,34 @@ We will consider different computational models according to the available level
 
 Atomic R/W registers are storage units that can be accessed through two operations (READ and WRITE) such that
 1. Each invocation of an operation
-	- locks instantaneous (it can be depicted as a single point on the timelinethere exist $t : OpInv \to R+$)
+	- locks instantaneous (it can be depicted as a single point on the timeline: there exist $t : OpInv \to R+$)
 	- may be located in any point between its starting and ending time
-	- does not happen together with any other operation
-2. Every READ returns the closest preceeding value written in the register, or the initial value (if no WRITE has occurred).
+	- does not happen together with any other operation ($t$ is injective)
+2. Every READ returns the closest preceding value written in the register, or the initial value (if no WRITE has occurred).
+
+### Peterson algorithm (for two processes)
+Let's try to enforce MUTEX with just 2 processes.
+
+1st attempt:
+```
+lock(i) :=
+	AFTER_YOU <- i
+	wait AFTER_YOU != i
+	return
+
+unlock(i) :=
+	return
+```
+This protocol satisfies MUTEX, but suffers from deadlock (if one process never locks).
+
+2nd attempt:
+```
+Initialize FLAG[0] and FLAG[1] to down
+lock(i) :=
+	AFTER_YOU <- i
+	wait AFTER_YOU != i
+	return
+
+unlock(i) :=
+	return
+```