marcorealacci/master-degree-notes
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

vault backup: 2025-04-30 19:13:22

Browse source
This commit is contained in:
Marco Realacci 2025-04-30 19:13:22 +02:00
parent f6bcd98780
commit f12ec77086
1 changed files with 10 additions and 0 deletions
Download patch file Download diff file Expand all files Collapse all files

10
Concurrent Systems/notes/14 Checking bisimilarity, an inference system.md
View file

@ -7,6 +7,8 @@ Inference system = axioms + inference rules
- completeness: whatever is bisimilar, it can be inferred - completeness: whatever is bisimilar, it can be inferred
#### Axioms & Rules for Strong Bisimilarity #### Axioms & Rules for Strong Bisimilarity
just what we've seen so far, literally.
![350](images/Pasted%20image%2020250429082812.png) ![350](images/Pasted%20image%2020250429082812.png)
quite obvious. quite obvious.
@ -15,11 +17,19 @@ basically we can let the left or the right process evolve, leaving the other unc
![350](images/Pasted%20image%2020250429083129.png) ![350](images/Pasted%20image%2020250429083129.png)
- if a process does not perform any action, a restriction won't do anything - if a process does not perform any action, a restriction won't do anything
- restriction is distributive
- if the process does not do the restricted action, the restriction won't do anything - if the process does not do the restricted action, the restriction won't do anything
- what if we restrict on the actual action? - what if we restrict on the actual action?
- well, then the process becomes 0 - well, then the process becomes 0
![350](images/Pasted%20image%2020250429083455.png) ![350](images/Pasted%20image%2020250429083455.png)
- if $P = P \land P = Q => Q = P$ (it's transitive :o)
- the same happens with contexts
#### Soundness theorem: $\vdash P=Q \implies P \sim Q$
*Proof:*
If $\vdash LHS=RHS$e need to consider the relation $\{ LHS,RHS \}$
![](images/Pasted%20image%2020250429083535.png) ![](images/Pasted%20image%2020250429083535.png)
$P$ is in standard form if and only if $P \triangleq \sum_{i}\alpha_{i}P_{i}$ and $\forall_{i}P_{i}$ is in standard form. $P$ is in standard form if and only if $P \triangleq \sum_{i}\alpha_{i}P_{i}$ and $\forall_{i}P_{i}$ is in standard form.