From 7fa6feb7f01bf33e8ca9bad886bad78c603d99d4 Mon Sep 17 00:00:00 2001
From: Marco Realacci <marco@marcorealacci.me>
Date: Mon, 28 Apr 2025 09:17:04 +0200
Subject: [PATCH] vault backup: 2025-04-28 09:17:04

---
 .obsidian/workspace.json                           | 4 ++--
 Concurrent Systems/notes/13 - Weak Bisimilarity.md | 9 +++++++++
 2 files changed, 11 insertions(+), 2 deletions(-)

diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index f072ed3..f83ad92 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -211,11 +211,11 @@
       "companion:Toggle completion": false
     }
   },
-  "active": "6c4a39240e6da514",
+  "active": "56150e6df7869900",
   "lastOpenFiles": [
+    "Concurrent Systems/slides/class 13.pdf",
     "Concurrent Systems/notes/13 - Weak Bisimilarity.md",
     "Pasted image 20250428085837.png",
-    "Concurrent Systems/slides/class 13.pdf",
     "Pasted image 20250428085410.png",
     "Pasted image 20250428084340.png",
     "Pasted image 20250428083727.png",
diff --git a/Concurrent Systems/notes/13 - Weak Bisimilarity.md b/Concurrent Systems/notes/13 - Weak Bisimilarity.md
index bed02ee..7a51762 100644
--- a/Concurrent Systems/notes/13 - Weak Bisimilarity.md	
+++ b/Concurrent Systems/notes/13 - Weak Bisimilarity.md	
@@ -85,3 +85,12 @@ 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)
 
+This is a family of relations:
+- 3 pairs of the second form (one for every x)
+- 9 pairs of the fifth form (one for every x and y)
+- 3 pairs of the sixth form
+- 3 pairs of the seventh form
+
+Furthermore, we should also consider commutativity of parallel in pairs of the second, third, fourth, sixth, seventh and eighth form.
+
+Thus, R is actually made up of 1+6+2+2+9+6+6+2=34 pairs.