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Concurrent Systems/notes/6a - Alternatives to Atomicity.md

@@ -1,5 +1,6 @@
 Let us define $op ->_{proc} op'$ to hold whenever there exists a process p that issues both operations with `res[op]` happening before `inv[op']`.
 
+### Sequential consistency
 **Def:** a complete history is sequentially consistent if there exists a sequential history $𝑆$ s.t.
 ![[Pasted image 20250324082534.png]]
 
@@ -17,4 +18,17 @@ In isolation, both processes are sequentially consistent.
 
 However, no total order on the previous 6 operations respects the semantics of a queue:
 	- if p1 receives b' from Q'.deq, we have that Q'.enq(a'), must arrive after Q'.enq(b')
-	- to respect $\to_{proc}$
+	- to respect $\to_{proc}$, also the remaining behavior of p2 must arrive after
+	- hence, Q.enq(a) arrived before Q.enq(b) and so it is not possible for p2 to receive b from its Q.deq.
+
+Hence, we have two histories that are sequentially consistent but whose composition cannot be sequentially consistent $\to$ **no compositionality!**
+
+### Serializability
+(typical notion in databases)
+
+- instead of processes, we have transactions
+- consequently, we have also two other kinds of events: `abort(t)` and `commit(t)`
+	- in every history, we have at most one of these events for every transaction
+	- if the history is complete, we must have exactly one of these events for transaction
+- a sequential history is formed by committed transactions only
+