vault backup: 2025-04-15 08:45:18

.obsidian/workspace.json

@@ -28,12 +28,12 @@
             "state": {
               "type": "markdown",
               "state": {
-                "file": "Concurrent Systems/notes/13 -.md",
+                "file": "Concurrent Systems/notes/13 - CCS cose varie.md",
                 "mode": "source",
                 "source": false
               },
               "icon": "lucide-file",
-              "title": "13 -"
+              "title": "13 - CCS cose varie"
             }
           }
         ],
@@ -229,9 +229,9 @@
   "active": "9d3f25b0eb9b478f",
   "lastOpenFiles": [
     "Concurrent Systems/slides/class 12.pdf",
-    "Concurrent Systems/notes/13 -.md",
-    "Pasted image 20250415082906.png",
+    "Concurrent Systems/notes/13 - CCS cose varie.md",
     "Concurrent Systems/notes/12 - Calculus of communicating system.md",
+    "Pasted image 20250415082906.png",
     "Concurrent Systems/notes/11 - LTSs and Bisimulation.md",
     "Concurrent Systems/notes/images/Pasted image 20250414164549.png",
     "Concurrent Systems/notes/images/Pasted image 20250414181443.png",

Concurrent Systems/notes/13 - CCS cose varie.md

@@ -13,7 +13,7 @@ This means that the implementation and the specification do coincide. To show th
 ![](../../Pasted%20image%2020250415082906.png)
 
 ## Restrictions
-**Proposition:** a.P\a ∼ 0
+**Proposition:** $a.P \textbackslash a ∼ 0$
 *Proof:*
 - S = {(a.P\a , 0)} is a bisimulation
 
@@ -21,6 +21,11 @@ Which challenges can (a.P)\a have?
 - a.P can only perform a (and become P)
 - however, because of restriction, a.P\a is stuck
 
- No challenge from a.P\a, nor from 0 à bisimilar!
+ No challenge from a.P\a, nor from 0 -> bisimilar!
 
-**Proposition:** 
+**Proposition:** $\bar{a}.P \textbackslash a ∼ 0$
+*Proof is similar.*
+
+## Idempotency of Sum
+**Proposition:** $α.P+α.P+M ∼ α.P+M$
+*Proof:*