vault backup: 2025-04-14 16:45:00

Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md

@@ -90,33 +90,23 @@ Sure Marco! Let's go step-by-step through the **CCS process transition example**
 
 ---
 
-## 📘 Definitions
+#### Example
+##### 📘 Definitions
 
 We start with the following **process definitions**:
 
-- A≜a.A′A \triangleq a.A'
+- $A \triangleq a.A'$
+- $A' \triangleq \bar{b}.A$
+- $B \triangleq b.B'$
+- $B' \triangleq \bar{c}.B$
 
-- A′≜bˉ.AA' \triangleq \bar{b}.A
-    
-- B≜b.B′B \triangleq b.B'
-    
-- B′≜cˉ.BB' \triangleq \bar{c}.B
-    
-
-Our **initial process** is:  
-A∣BA \mid B
-
----
-
-## ▶️ Step 1: Transition from A
+Our **initial process** is: $A \mid B$
 
+##### ▶️ Step 1: Transition from A
 From the definition:
 
-- A≜a.A′A \triangleq a.A'  
-    So we can do:
-    
-
-A→aA′A \xrightarrow{a} A'
+- $A \triangleq a.A'$
+	- So we can do: $A \xrightarrow{a} A'$ (A consumes )
 
 Using the **parallel rule** for the left-hand side: