From 83dcccfc7aa02b24064a129f38d0870d9a6c5693 Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Mon, 28 Apr 2025 08:57:04 +0200 Subject: [PATCH] vault backup: 2025-04-28 08:57:04 --- .obsidian/workspace.json | 2 +- .../notes/13 - Weak Bisimilarity.md | 21 ++++++++++++++++-- Pasted image 20250428085410.png | Bin 0 -> 46582 bytes 3 files changed, 20 insertions(+), 3 deletions(-) create mode 100644 Pasted image 20250428085410.png diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 0732644..251b622 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -215,6 +215,7 @@ "lastOpenFiles": [ "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", diff --git a/Concurrent Systems/notes/13 - Weak Bisimilarity.md b/Concurrent Systems/notes/13 - Weak Bisimilarity.md index e58cc45..da46ebb 100644 --- a/Concurrent Systems/notes/13 - Weak Bisimilarity.md +++ b/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: $$A\triangleq i_{E}.A'+i_{M}. A'+i_{D}.A'$$ -$$A' \triangleq$$ \ No newline at end of file +$$A' \triangleq \bar{o}.A$$ +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 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