diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 83d1dc2..c6d84f8 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -68,7 +68,8 @@ "title": "class 11" } } - ] + ], + "currentTab": 1 } ], "direction": "vertical" @@ -238,10 +239,10 @@ "companion:Toggle completion": false } }, - "active": "84845736e00d5c98", + "active": "364a7591f14f033a", "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 20250414173011.png", "Pasted image 20250414164549.png", "Concurrent Systems/notes/images/Pasted image 20250414082824.png", 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 f01eddd..526cf69 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 @@ -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. \ No newline at end of file