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 072ccb2..dfb2183 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 @@ -159,14 +159,19 @@ What if we restrict on b? ![](../../Pasted%20image%2020250414173011.png) +##### Example 1: +as $a$ is not in $\{b, \bar{b}\}$, we will see the transitions: +$$ +\frac{\frac{\frac{a.A' \xrightarrow{a} A' \quad A \triangleq a.A'}{A \xrightarrow{a} A'}} +{{A \mid B \xrightarrow{a} A' \mid B}}a \not \in \{b, \bar{b}\}}{{(A \mid B) \setminus b \xrightarrow{a} (A' \mid B) \setminus b}} +$$ + +Split in separate peaces for improved readability: $$\frac{a.A' \xrightarrow{a} A' \quad A \triangleq a.A'}{A \xrightarrow{a} A'} \quad \frac{A \xrightarrow{a} A'}{A \mid B \xrightarrow{a} A' \mid B} \quad \frac{A \mid B \xrightarrow{a} A' \mid B \quad a \notin \{b, \bar{b}\}}{(A \mid B) \setminus b \xrightarrow{a} (A' \mid B) \setminus b}$$ -$$ - - - -$$ \ No newline at end of file +##### Example 2: +as $b$ is in \ No newline at end of file