From 1103ed5d9f04e185fdc99f20b4d338b04465a682 Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Mon, 28 Apr 2025 08:47:04 +0200 Subject: [PATCH] vault backup: 2025-04-28 08:47:04 --- .obsidian/workspace.json | 5 ++--- .../notes/13 - Weak Bisimilarity.md | 18 +++++++++++++++--- Pasted image 20250428084340.png | Bin 0 -> 71115 bytes 3 files changed, 17 insertions(+), 6 deletions(-) create mode 100644 Pasted image 20250428084340.png diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 8690022..0732644 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -213,9 +213,10 @@ }, "active": "56150e6df7869900", "lastOpenFiles": [ - "Pasted image 20250428083727.png", "Concurrent Systems/slides/class 13.pdf", "Concurrent Systems/notes/13 - Weak Bisimilarity.md", + "Pasted image 20250428084340.png", + "Pasted image 20250428083727.png", "Concurrent Systems/notes/12 - Calculus of communicating system.md", "Concurrent Systems/slides/class 12.pdf", "Concurrent Systems/notes/12b - CCS cose varie.md", @@ -231,8 +232,6 @@ "Concurrent Systems/notes/images/Pasted image 20250414082824.png", "Concurrent Systems/notes/images/Pasted image 20250414152300.png", "Concurrent Systems/notes/images/Pasted image 20250414152247.png", - "Concurrent Systems/notes/images/Pasted image 20250414152234.png", - "Concurrent Systems/notes/images/Pasted image 20250414152221.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 6a9bac0..b875d53 100644 --- a/Concurrent Systems/notes/13 - Weak Bisimilarity.md +++ b/Concurrent Systems/notes/13 - Weak Bisimilarity.md @@ -36,6 +36,18 @@ $\approx$ is a *Proof:* take the symmetric closure of the following relations, that can be easily shown to be weak simulations: -1. $S = \{ P,\tau.P \}\cup Id$ -2. $S=\{ M+N+\tau.N,M+\tau.N \}\cup Id$ -3. $S=\\{ (M+\alpha.P+) \}$ \ No newline at end of file +1. $S = \{ (P,\tau.P )\}\cup Id$ +2. $S=\{ (M+N+\tau.N,M+\tau.N )\}\cup Id$ +3. $S=\{ ((M+\alpha.P+\alpha.(N+\tau.P), M+\alpha.(N+\tau.P)) \} \cup Id$ + +#### Weak bisimilarity abstracts from any $\tau$ +![](../../Pasted%20image%2020250428084340.png) + +**There exists no weak bisimulation S that contains (P, Q).** +*Proof:* +By contr. suppose that a bisimulation exists +Since Q −τ→ b.0, there must exist a P’ such that P ⇒ P and (P,b.0) ∈ S The only P that satisfies P ⇒ P’ is P itself +hence it should be (P,b.0) ∈ S + +Contradiction: P can perform a whereas b.0 cannot !! +Similarly, P/R and Q/R are NOT weakly bisimilar \ No newline at end of file diff --git a/Pasted image 20250428084340.png b/Pasted image 20250428084340.png new file mode 100644 index 0000000000000000000000000000000000000000..6e370fabfc0f172fdbd61fd619cc5b3d97f1a8f5 GIT binary patch literal 71115 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