From e35e647ca7ba528f0cc83c22286bc73a0fa7e93f Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Mon, 28 Apr 2025 09:02:04 +0200 Subject: [PATCH] vault backup: 2025-04-28 09:02:04 --- .obsidian/workspace.json | 1 + .../notes/13 - Weak Bisimilarity.md | 10 +++++++++- Pasted image 20250428085837.png | Bin 0 -> 116872 bytes 3 files changed, 10 insertions(+), 1 deletion(-) create mode 100644 Pasted image 20250428085837.png diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 251b622..6581465 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -213,6 +213,7 @@ }, "active": "56150e6df7869900", "lastOpenFiles": [ + "Pasted image 20250428085837.png", "Concurrent Systems/slides/class 13.pdf", "Concurrent Systems/notes/13 - Weak Bisimilarity.md", "Pasted image 20250428085410.png", diff --git a/Concurrent Systems/notes/13 - Weak Bisimilarity.md b/Concurrent Systems/notes/13 - Weak Bisimilarity.md index da46ebb..bed02ee 100644 --- a/Concurrent Systems/notes/13 - Weak Bisimilarity.md +++ b/Concurrent Systems/notes/13 - Weak Bisimilarity.md @@ -76,4 +76,12 @@ There is only one special and only one general machine that the workers have to 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: -$$Workers \triangleq (W|W|G|S) \setminus_{\{rg,rs,lg,ls \}}$$ \ No newline at end of file +$$Workers \triangleq (W|W|G|S) \setminus_{\{rg,rs,lg,ls \}}$$ +We now want to show that: +$$Factory \approx Workers$$ +i.e., that the specification and the implementation of the factory behave the same (apart from internal actions). + +Let N denote {rg,rs,lg,ls} and x,y ∊ {E,M,D} +We can prove that the following relation is a weak bisimulation: +![](../../Pasted%20image%2020250428085837.png) + diff --git a/Pasted image 20250428085837.png b/Pasted image 20250428085837.png new file mode 100644 index 0000000000000000000000000000000000000000..40c2ffae7e78e59573ecf9f8f6149974ea513eba GIT binary patch literal 116872 zcma&ObzIfmwlA#G-JQ}UAf3`FQX(ZvNJ~q1cQ;Bm(hZW*DXoAYEvQI?fPiJ9kA;@4;6ldWUZR z2hBlI@6DY%*nPME+)ZJ}rnqy5_KuRQl$LwuZij_C!53oA3NocsuYD}cfdRsq*E_iQ z%KnpR$oKAd->0O_Lq?^dP|OSc_S#ZH>JBp~tg7;5p7@}BGLhfj3Sq$-g_=9RPRcm0LF7P~p4PUxdg}g(xeJ!Tc 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