vault backup: 2025-03-24 08:49:22

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

@@ -32,3 +32,9 @@ Hence, we have two histories that are sequentially consistent but whose composit
 	- if the history is complete, we must have exactly one of these events for transaction
 - a sequential history is formed by committed transactions only
 
+**Def:** a complete history $\hat{H}$ is **serializable** if there exists a sequential history $\hat{S}$ s.t.
+1. $\forall X : \hat{S}|_X \in semantics(X)$
+2. $S = \{e \in H : e \in t \ in committedTrans(\hat{H})\}$
+3. $\to_{trans} \subseteq \to_{S}$ where $\to_{trans}$ is defined like $\to_{proc}$ in sequential consistency.
+
+It is a more general notion than linearizability, **but it is not compositional** (consider the previous example but with transactions instead of processes).