From 9db7dc58419a6ca9e85e0cd3bb737f716c8e4eb2 Mon Sep 17 00:00:00 2001
From: Marco Realacci <marco@marcorealacci.me>
Date: Wed, 30 Apr 2025 17:13:22 +0200
Subject: [PATCH] vault backup: 2025-04-30 17:13:22

---
 .obsidian/workspace.json                      | 21 +++++--------------
 .../notes/13 - Weak Bisimilarity.md           |  7 ++++++-
 2 files changed, 11 insertions(+), 17 deletions(-)

diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index 47ce0ab..8d8779b 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -20,18 +20,6 @@
               "icon": "lucide-file",
               "title": "13 - Weak Bisimilarity"
             }
-          },
-          {
-            "id": "4151b8cc103dc898",
-            "type": "leaf",
-            "state": {
-              "type": "pdf",
-              "state": {
-                "file": "Concurrent Systems/slides/class 13.pdf"
-              },
-              "icon": "lucide-file-text",
-              "title": "class 13"
-            }
           }
         ]
       }
@@ -90,7 +78,8 @@
       }
     ],
     "direction": "horizontal",
-    "width": 309.5
+    "width": 309.5,
+    "collapsed": true
   },
   "right": {
     "id": "bc4b945ded1926e3",
@@ -204,10 +193,10 @@
   },
   "active": "ec8d1a91f1f0cc7e",
   "lastOpenFiles": [
-    "Concurrent Systems/notes/14.md",
-    "Concurrent Systems/notes/13 - Weak Bisimilarity.md",
-    "Concurrent Systems/notes/12b - CCS cose varie.md",
     "Concurrent Systems/slides/class 13.pdf",
+    "Concurrent Systems/notes/13 - Weak Bisimilarity.md",
+    "Concurrent Systems/notes/14.md",
+    "Concurrent Systems/notes/12b - CCS cose varie.md",
     "Concurrent Systems/notes/12 - Calculus of communicating system.md",
     "Concurrent Systems/notes/images/Pasted image 20250415082906.png",
     "Concurrent Systems/slides/class 14.pdf",
diff --git a/Concurrent Systems/notes/13 - Weak Bisimilarity.md b/Concurrent Systems/notes/13 - Weak Bisimilarity.md
index ae60fc9..7927510 100644
--- a/Concurrent Systems/notes/13 - Weak Bisimilarity.md	
+++ b/Concurrent Systems/notes/13 - Weak Bisimilarity.md	
@@ -109,4 +109,9 @@ Every component can be in three states:
 - A (waiting for being habilitated to extraction)
 - B (habilitated, with the possibility of being extracted or of habilitating the next component)
 - C (extracted, waiting to externally communicate its value and start the process again): $$A_{i}=a_{i}.B_{i} \quad B_{i}=\tau.C_{i}+\bar{a}_{(i \space mod \space n)+1}.A_{i} \quad C_{i}=\bar{p}_{i}.B_{i}$$
-In pratica ogni volta o estrae di nuovo "se stesso" oppure "abilita" il componente successivo.
\ No newline at end of file
+In pratica ogni volta o estrae di nuovo "se stesso" oppure "abilita" il componente successivo.
+
+Implementation: $$Impl \triangleq (B_{1}|A_{2}|\dots|An)$$
+basically we need to have an initially habilitated process, which can be any (the first one in our case).
+
+This will generate the LTS:
\ No newline at end of file