vault backup: 2025-04-14 18:19:02

.obsidian/workspace.json

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Concurrent Systems/notes/12 - Calculus of communicating system.md

@@ -7,6 +7,9 @@
 	- Parallel composition, with interleaving semantics
 	- Producer/consumer paradigm
 
+>[!note] Suggested reading
+>https://en.wikipedia.org/wiki/Calculus_of_communicating_system
+
 Given a set of names N (that denote events)
 - $a (\in N)$ denotes consumption of event a
 - $\bar{a}$ (for $a \in N$) denotes production of event a
@@ -19,7 +22,6 @@ The set of actions we shall consider is: $N \cup \bar{N} \cup \{\tau\}$
 It is also useful to force some processes of the system to synchronize between them (without the possibility of showing to the outside some actions)
 
 The restriction operator P\a restricts the scope of name a to process P (a is visible only from within P)
-https://en.wikipedia.org/wiki/Calculus_of_communicating_system
 
 This is similar to local variables in a procedure of an imperative program
 
@@ -91,7 +93,7 @@ Sure Marco! Let's go step-by-step through the **CCS process transition example**
 ---
 
 #### Example
-![](../../Pasted%20image%2020250414164549.png)
+![](images/Pasted%20image%2020250414164549.png)
 
 #### Example, but explained
 ##### 📘 Definitions
@@ -157,7 +159,7 @@ The usefulness of the parallel is two-fold:
 ### Restriction
 What if we restrict on b?
 
-![](../../Pasted%20image%2020250414173011.png)
+![](images/Pasted%20image%2020250414173011.png)
 
 ##### Example 1:
 since $a$ is not in $\{b, \bar{b}\}$, we will see the transitions:
@@ -184,4 +186,4 @@ This time I won't split it in separate pieces since I don't feel like doing it,
 - Notice that the τ, even if it has been generated by synchronizing on b, it is still present after applying the restriction on b!
 	- the purpose of the τ is exactly to signal that a synchronization has happened but to hide the event on which the involved processed synchronized.
 
-- In general, it is possible that whole states disappear upon restriction of some names: this would be the case, e.g., if we consider the LTS arising from $(A’ | B)\setminus a,b$:![](../../Pasted%20image%2020250414181443.png)
+- In general, it is possible that whole states disappear upon restriction of some names: this would be the case, e.g., if we consider the LTS arising from $(A’ | B)\setminus a,b$ (restricting on both a and b):![](images/Pasted%20image%2020250414181443.png)