From 3a3639c6f7f554ee9d6b77dc53273aab1c2e39fb Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Tue, 29 Apr 2025 09:23:47 +0200 Subject: [PATCH] vault backup: 2025-04-29 09:23:47 --- .obsidian/workspace.json | 5 +++-- Concurrent Systems/notes/14.md | 9 ++++++++- Pasted image 20250429091959.png | Bin 0 -> 85328 bytes Pasted image 20250429092055.png | Bin 0 -> 186929 bytes Pasted image 20250429092305.png | Bin 0 -> 221299 bytes 5 files changed, 11 insertions(+), 3 deletions(-) create mode 100644 Pasted image 20250429091959.png create mode 100644 Pasted image 20250429092055.png create mode 100644 Pasted image 20250429092305.png diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index e4a5aea..bf23ca8 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -213,6 +213,9 @@ }, "active": "ec8d1a91f1f0cc7e", "lastOpenFiles": [ + "Pasted image 20250429092305.png", + "Pasted image 20250429092055.png", + "Pasted image 20250429091959.png", "Concurrent Systems/slides/class 14.pdf", "Concurrent Systems/notes/14.md", "Pasted image 20250429091029.png", @@ -223,8 +226,6 @@ "Pasted image 20250429083535.png", "Pasted image 20250429083455.png", "Pasted image 20250429083129.png", - "Pasted image 20250429082905.png", - "Pasted image 20250429082812.png", "Concurrent Systems/notes/13 - Weak Bisimilarity.md", "Concurrent Systems/slides/class 13.pdf", "Concurrent Systems/notes/12 - Calculus of communicating system.md", diff --git a/Concurrent Systems/notes/14.md b/Concurrent Systems/notes/14.md index 95c203d..6ca3f48 100644 --- a/Concurrent Systems/notes/14.md +++ b/Concurrent Systems/notes/14.md @@ -53,4 +53,11 @@ exercise: prove the weak bisimilarity Let us consider the parallel of processes M and R, by using the axiom for parallel, we have $$\vdash M|R=put.(\overline{go}|R)+go.(M|\overline{rcv})$$ By using the same axiom to the parallel of the three processes, we obtain -$$\vdash S|(M|R)=send.(\overline{put}|(M|R))+put.(\overline{go})$$ \ No newline at end of file +$$\vdash S|(M|R)=send.(\overline{put}|(M|R))+put.(\overline{go}|R|S)+go.(\overline{rcv}|S|M)$$ +By restricting *put* and *go*, and by using the second axiom for restriction, we have that: +![](../../Pasted%20image%2020250429091959.png) + +We now apply the third axiom for restriction to the three summands: +![](../../Pasted%20image%2020250429092055.png) +![](../../Pasted%20image%2020250429092305.png) + diff --git a/Pasted image 20250429091959.png b/Pasted image 20250429091959.png new file mode 100644 index 0000000000000000000000000000000000000000..1fd6c91d39c79587f1004163f9e09081d1e3353c GIT binary patch literal 85328 zcmV)(K#RYLP)z0ssI2Nxnz%00009a7bBm000ie z000ie0hKEb8vp&((xp&+|~)^b|xsO_DZ<8pTA z=2i`Pt4KS3Iexgm;EZ-=_lbLZORn*jq#cj8w>LApqgqT$bT`lqpil)>D6O(mYZc1< z?72roW&zb=dVofA(LNY-A~G_+s<@OqX(UKhsUvdY0R+ny|WBrt>YYHa*Szx z#5{b*GKic*x?*sQX7^vDbL3O>@6Z+Wxz3LRque_LxAmpxOw4}#tFb>Kmc<88puc75 zV!|B!A!CT`^~J&ewF)Lcvxz7gEUN--TThIIC?0ItF9e1~# 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