vault backup: 2025-04-28 08:57:04

.obsidian/workspace.json

@@ -215,6 +215,7 @@
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     "Concurrent Systems/slides/class 13.pdf",
     "Concurrent Systems/notes/13 - Weak Bisimilarity.md",
+    "Pasted image 20250428085410.png",
     "Pasted image 20250428084340.png",
     "Pasted image 20250428083727.png",
     "Concurrent Systems/notes/12 - Calculus of communicating system.md",
@@ -231,7 +232,6 @@
     "Concurrent Systems/notes/images/Pasted image 20250414173011.png",
     "Concurrent Systems/notes/images/Pasted image 20250414082824.png",
     "Concurrent Systems/notes/images/Pasted image 20250414152300.png",
-    "Concurrent Systems/notes/images/Pasted image 20250414152247.png",
     "HCIW/notes/3 - Beacons.md",
     "HCIW/slides/Zooming interfaces.pdf",
     "HCIW/slides/Gestural interaction.pdf",

Concurrent Systems/notes/13 - Weak Bisimilarity.md

@@ -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:
+$$Workers \triangleq (W|W|G|S) \setminus_{\{rg,rs,lg,ls  \}}$$