diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index dc03cc2..f97a7e7 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -238,10 +238,10 @@ "companion:Toggle completion": false } }, - "active": "84845736e00d5c98", + "active": "2882ba3b76891dd0", "lastOpenFiles": [ - "Concurrent Systems/slides/class 12.pdf", "Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md", + "Concurrent Systems/slides/class 12.pdf", "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 cb282b0..48f1efc 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 @@ -130,18 +130,13 @@ $$A' \mid B \xrightarrow{\tau} A \mid B'$$ ##### ▶️ Step 3: Transition from B' From the definition: -- $BB' \triangleq \bar{c}.B$ - - So: B′→cˉBB' \xrightarrow{\bar{c}} B +- $B' \triangleq \bar{c}.B$ + - So: $B' \xrightarrow{\bar{c}} B$ Now use the **right parallel rule**: - -B′→cˉBA∣B′→cˉA∣B\frac{B' \xrightarrow{\bar{c}} B}{A \mid B' \xrightarrow{\bar{c}} A \mid B} - +$$\frac{B' \xrightarrow{\bar{c}} B}{A \mid B' \xrightarrow{\bar{c}} A \mid B}$$ ✅ **Third transition:** - -A∣B′→cˉA∣BA \mid B' \xrightarrow{\bar{c}} A \mid B - ---- +$$A \mid B' \xrightarrow{\bar{c}} A \mid B$$ ## 🔄 Full Transition Path