vault backup: 2025-04-14 16:35:00

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Marco Realacci 2025-04-14 16:35:00 +02:00
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@ -65,19 +65,16 @@ $$\frac{P_2 \xrightarrow{\alpha} P_2'}{P_1 \mid P_2 \xrightarrow{\alpha} P_1 \mi
$$\frac{P_1 \xrightarrow{a} P_1' \quad P_2 \xrightarrow{\bar{a}} P_2'}{P_1 \mid P_2 \xrightarrow{\tau} P_1' \mid P_2'}$$ $$\frac{P_1 \xrightarrow{a} P_1' \quad P_2 \xrightarrow{\bar{a}} P_2'}{P_1 \mid P_2 \xrightarrow{\tau} P_1' \mid P_2'}$$
> If one process can **send** (`a`) and the other can **receive** (`ā`), they **synchronize**, and the result is an **internal (τ)** action. This models communication. > If one process can **send** (`a`) and the other can **receive** (`ā`), they **synchronize**, and the result is an **internal (τ)** action. This models communication.
## 🧠 Summary Table: ##### 🧠 Summary Table:
|Rule Type|Description| | Rule Type | Description |
|---|---| | ---------------------- | ----------------------------------------------------------- |
|Choice|Select one summand to act| | Choice | Select one summand to act |
|Process Call|Expand definition by substituting parameters| | Process Call | Expand definition by substituting parameters |
|Restriction|Only allows transitions not involving the restricted action| | Restriction | Only allows transitions not involving the restricted action |
|Parallel (independent)|A single component acts, the other stays the same| | Parallel (independent) | A single component acts, the other stays the same |
|Parallel (sync)|Two components synchronize to produce τ| | Parallel (sync) | Two components synchronize to produce τ |
---
Let me know if you want to **trace an example** using these rules step-by-step — like watching how a CCS process evolves over time. It's super helpful to solidify the concepts!
![](images/Pasted%20image%2020250414104010.png) ![](images/Pasted%20image%2020250414104010.png)