vault backup: 2025-04-15 09:05:18

.obsidian/workspace.json

@@ -230,6 +230,7 @@
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     "Concurrent Systems/slides/class 12.pdf",
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+    "Pasted image 20250415090109.png",
     "Concurrent Systems/notes/12 - Calculus of communicating system.md",
     "Pasted image 20250415082906.png",
     "Concurrent Systems/notes/11 - LTSs and Bisimulation.md",
@@ -242,7 +243,6 @@
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     "Concurrent Systems/notes/images/Pasted image 20250414152234.png",
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     "HCIW/notes/3 - Beacons.md",
     "HCIW/slides/Zooming interfaces.pdf",
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Concurrent Systems/notes/13 - CCS cose varie.md

@@ -47,5 +47,12 @@ Let's go!
 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
+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:
+![200](../../Pasted%20image%2020250415090109.png)
+
+where C is a context (i.e., a process with a hole ☐), P is a process, and $C[P]$ denotes filling the hole with P
+
+Example: $$if \space C = (☐ | Q) \textbackslash a, \space then \space C[P] = (P | Q) \textbackslash a$$
+The set C of CCS contexts is given by the following grammar:
+$$C ::= ☐ \space | \space C|P \space | $$