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Marco Realacci 2025-04-14 17:50:00 +02:00
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Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md
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@ -160,13 +160,13 @@ 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:
since $a$ 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:
Split in separate peaces for better readability:
$$\frac{a.A' \xrightarrow{a} A' \quad A \triangleq a.A'}{A \xrightarrow{a} A'}
\quad
\frac{A \xrightarrow{a} A'}{A \mid B \xrightarrow{a} A' \mid B}
@ -174,7 +174,7 @@ $$\frac{a.A' \xrightarrow{a} A' \quad A \triangleq a.A'}{A \xrightarrow{a} A'}
\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}$$
##### Example 2:
as $b$ is in $\{b, \bar{b}\}$, we will NOT see the transitions:
since $b$ is in $\{b, \bar{b}\}$, we will NOT see the transitions:
$$\frac{\frac{\frac{b.B' \xrightarrow{b} B' \quad B \triangleq b.B'}{B \xrightarrow{b} B'}}
{{A \mid B \xrightarrow{b} A \mid B'}}b \in \{b, \bar{b}\}}{{(A \mid B) \setminus b}}$$
This time I won't split it in separate pieces since I don't feel like doing it, just buy glasses.