vault backup: 2025-04-15 09:00:18

Concurrent Systems/notes/13 - CCS cose varie.md

@@ -42,3 +42,10 @@ P –β–> P’ (challenge and reply), but we don't have (P', P') in S.
 
 So let's try with: $$S = \{ (α.P+α.P+M , α.P+M) \} ∪ Id$$
 Let's go!
+
+## Congruence
+One of the main aims of an equivalence notion between processes is to make equational reasonings of the kind: “if P and Q are equivalent, then they can be interchangeably used in any execution context”.
+
+This feature on an equivalence makes it a *congruence*
+Not all equivalences are necessarily congruences (even though most of them are
+To properly define a congruence, we first need to define an execution context, and then what it means to run a process in a context. Intuitively: