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Marco Realacci 2025-04-14 17:50:00 +02:00
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commit 9ea4a2b42f
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7
.obsidian/workspace.json vendored
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@ -68,7 +68,8 @@
"title": "class 11" "title": "class 11"
} }
} }
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"direction": "vertical" "direction": "vertical"
@ -238,10 +239,10 @@
"companion:Toggle completion": false "companion:Toggle completion": false
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"Concurrent Systems/slides/class 12.pdf",
"Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md", "Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md",
"Concurrent Systems/slides/class 12.pdf",
"Pasted image 20250414173011.png", "Pasted image 20250414173011.png",
"Pasted image 20250414164549.png", "Pasted image 20250414164549.png",
"Concurrent Systems/notes/images/Pasted image 20250414082824.png", "Concurrent Systems/notes/images/Pasted image 20250414082824.png",

6
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) ![](../../Pasted%20image%2020250414173011.png)
##### Example 1: ##### 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'}} \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}} {{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:
$$\frac{a.A' \xrightarrow{a} A' \quad A \triangleq a.A'}{A \xrightarrow{a} A'} $$\frac{a.A' \xrightarrow{a} A' \quad A \triangleq a.A'}{A \xrightarrow{a} A'}
\quad \quad
\frac{A \xrightarrow{a} A'}{A \mid B \xrightarrow{a} A' \mid B} \frac{A \xrightarrow{a} A'}{A \mid B \xrightarrow{a} A' \mid B}
@ -174,7 +174,7 @@ $$\frac{a.A' \xrightarrow{a} A' \quad A \triangleq a.A'}{A \xrightarrow{a} A'}
\frac{A \mid B \xrightarrow{a} A' \mid B \quad a \notin \{b, \bar{b}\}}{(A \mid B) \setminus b \xrightarrow{a} (A' \mid B) \setminus b}$$ \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}$$
##### Example 2: ##### Example 2:
as $b$ is in $\{b, \bar{b}\}$, we will NOT see the transitions: since $b$ is in $\{b, \bar{b}\}$, we will NOT see the transitions:
$$\frac{\frac{\frac{b.B' \xrightarrow{b} B' \quad B \triangleq b.B'}{B \xrightarrow{b} B'}} $$\frac{\frac{\frac{b.B' \xrightarrow{b} B' \quad B \triangleq b.B'}{B \xrightarrow{b} B'}}
{{A \mid B \xrightarrow{b} A \mid B'}}b \in \{b, \bar{b}\}}{{(A \mid B) \setminus b}}$$ {{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. This time I won't split it in separate pieces since I don't feel like doing it, just buy glasses.