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21
Concurrent Systems/notes/13 - Weak Bisimilarity.md
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@ -55,8 +55,25 @@ Similarly, P/R and Q/R are NOT weakly bisimilar
### EXAMPLE: Factory
A factory can handle three kinds of works: easy (E), medium (M), difficult (D).
An activity of the factory consists in receiving in input a work (of any kind) and in producing in output a manifactured work.
An activity of the factory consists in receiving in input a work (of any kind) and in producing in output a manufactured work.
The given specification of an activity is the following:
$$A\triangleq i_{E}.A'+i_{M}. A'+i_{D}.A'$$
$$A' \triangleq$$
$$A' \triangleq \bar{o}.A$$
where actions $i_{E}, i_{M}, i_{D}$ represents they input, and $\bar{o}$ represents the production of an output.
The factory is given by the parallel composition of two activities:
$$Factory \triangleq A|A$$
A possible implementation of this specification is obtained by having two workers that perform in parallel different kinds of work.
- For easy works, they don’t use any machinery
- For medium works, they can use either a special or a general machine
- For difficult works, they have to use the special machine.
There is only one special and only one general machine that the workers have to share.
![](../../Pasted%20image%2020250428085410.png)
where rg and rs are used to require the general/special machine, lg and ls are used to leave the general/special machine, and S and G implement a semaphore on the two different machines.
The resulting system is given by:
$$Workers \triangleq (W|W|G|S) \setminus_{\{rg,rs,lg,ls \}}$$