vault backup: 2025-04-14 09:24:56

.obsidian/workspace.json

@@ -238,10 +238,11 @@
       "companion:Toggle completion": false
     }
   },
-  "active": "364a7591f14f033a",
+  "active": "fbeaa35cc5a8abf1",
   "lastOpenFiles": [
-    "Concurrent Systems/notes/11 - LTSs and Bisimulation.md",
     "Concurrent Systems/slides/class 11.pdf",
+    "Concurrent Systems/notes/11 - LTSs and Bisimulation.md",
+    "Pasted image 20250414092202.png",
     "Concurrent Systems/slides/class 12.pdf",
     "Pasted image 20250414091528.png",
     "Pasted image 20250414091521.png",
@@ -268,7 +269,6 @@
     "Concurrent Systems/notes/2b - Round Robin algorithm.md",
     "\u0001.md",
     "Concurrent Systems/notes/images/Pasted image 20250405000438.png",
-    "Pasted image 20250405000428.png",
     "Concurrent Systems/a.md",
     "Concurrent Systems/notes/9 - Consensus.md",
     "Concurrent Systems/notes/8 - Enhancing Liveness Properties.md",

Concurrent Systems/notes/11 - LTSs and Bisimulation.md

@@ -110,3 +110,12 @@ The only ingredients we used to write down an LTS are:
 - non-deterministic choice (between a finite set of prefixed processes)
 - recursion
 
+To simplify process writing, we shall assume to have a finite set Id of processes identifiers and that the definitions we shall give will be parametric
+
+For every identifier (denoted with capital letters A,B,..), we shall assume a unique definition of the form $A(x1,x2,..,xn) := P$, where names x1,x2,..,xn are all distinct and all included in the names of P.
+
+Let us denote with P{b1/x1 . . . bn/xn} the process obtained from P by replacing name xi with name bi, for every i = 1,..., n.
+
+![](../../Pasted%20image%2020250414092202.png)
+
+The set of non