vault backup: 2025-04-30 19:48:22

Concurrent Systems/notes/14 Checking bisimilarity, an inference system.md

@@ -54,14 +54,15 @@ $P$ is in standard form if and only if $P \triangleq \sum_{i}\alpha_{i}P_{i}$ an
 	Now we fill the hole (*er bucio*) with $P_1$ and remove 1 from the set I (basically we pull it out from the summation): $$\alpha_{1}.P_{1} + \sum_{i \in I\setminus \{ 1 \}}\alpha_{i}P_{i}$$
 	Now we replace $P_1$ with $P_{1}'$ and obtain: $$=\alpha_{1}.P_{1}' + \sum_{i \in I\setminus \{ 1 \}}\alpha_{i}P_{i}$$
 	imagine doing this until you pulled everything out... Standard form!
-	
-3. 
 
 ![](images/Pasted%20image%2020250429085319.png)
 
 ### Axioms & Rules for Weak Bisimilarity
 ![](images/Pasted%20image%2020250429091029.png)
 
+#### Completeness theorem: $P \sim Q  \implies \vdash P=Q$
+
+
 #### Example
 A server for exchanging messages, in its minimal version, receives a request for sending messages and delivers the confirmation of the reception