From 7227bcbc96a10f4fc649def328da6b7d579059a2 Mon Sep 17 00:00:00 2001
From: Marco Realacci <marco@marcorealacci.me>
Date: Mon, 14 Apr 2025 17:05:00 +0200
Subject: [PATCH] vault backup: 2025-04-14 17:05:00

---
 .obsidian/workspace.json                       |  4 ++--
 .../12 - CCS (che non so cosa voglia dire).md  | 18 +++++-------------
 2 files changed, 7 insertions(+), 15 deletions(-)

diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index f97a7e7..dc03cc2 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -238,10 +238,10 @@
       "companion:Toggle completion": false
     }
   },
-  "active": "2882ba3b76891dd0",
+  "active": "84845736e00d5c98",
   "lastOpenFiles": [
-    "Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md",
     "Concurrent Systems/slides/class 12.pdf",
+    "Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md",
     "Pasted image 20250414164549.png",
     "Concurrent Systems/notes/images/Pasted image 20250414082824.png",
     "Concurrent Systems/notes/11 - LTSs and Bisimulation.md",
diff --git a/Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md b/Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md
index 6079b4b..cb282b0 100644
--- a/Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md	
+++ b/Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md	
@@ -123,23 +123,15 @@ From this, we can do:
 
 These actions **complement each other**, so we can apply the **synchronization rule**:
 
-A′→bˉAB→bB′A′∣B→τA∣B′\frac{A' \xrightarrow{\bar{b}} A \quad B \xrightarrow{b} B'}{A' \mid B \xrightarrow{\tau} A \mid B'}
+$$\frac{A' \xrightarrow{\bar{b}} A \quad B \xrightarrow{b} B'}{A' \mid B \xrightarrow{\tau} A \mid B'}$$
 
 ✅ **Second transition:**
+$$A' \mid B \xrightarrow{\tau} A \mid B'$$
 
-A′∣B→τA∣B′A' \mid B \xrightarrow{\tau} A \mid B'
-
----
-
-## ▶️ Step 3: Transition from B'
-
+##### ▶️ Step 3: Transition from B'
 From the definition:
-
-- B′≜cˉ.BB' \triangleq \bar{c}.B  
-    So:
-    
-
-B′→cˉBB' \xrightarrow{\bar{c}} B
+- $BB' \triangleq \bar{c}.B$
+	- So: B′→cˉBB' \xrightarrow{\bar{c}} B
 
 Now use the **right parallel rule**: