vault backup: 2025-04-14 09:29:56

.obsidian/workspace.json

@@ -238,10 +238,10 @@
       "companion:Toggle completion": false
     }
   },
-  "active": "fbeaa35cc5a8abf1",
+  "active": "364a7591f14f033a",
   "lastOpenFiles": [
-    "Concurrent Systems/slides/class 11.pdf",
     "Concurrent Systems/notes/11 - LTSs and Bisimulation.md",
+    "Concurrent Systems/slides/class 11.pdf",
     "Pasted image 20250414092202.png",
     "Concurrent Systems/slides/class 12.pdf",
     "Pasted image 20250414091528.png",

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

@@ -118,4 +118,13 @@ Let us denote with P{b1/x1 . . . bn/xn} the process obtained from P by replacing
 
 ![](../../Pasted%20image%2020250414092202.png)
 
-The set of non
+>[!def]
+>The set of non-deterministic processes is given by the following grammar:
+$$P::= \sum \alpha_{i}.P_{i} | A(a_{1}\dots a_{n})$$
+where I is a finite set of indices and $\alpha_{i} \in A$ for every $i \in I$.
+
+**Remark:** we now fuse together in a unique operator sequential composition and nondeterministic choice.
+If the index set $I$ is empty, then $\sum_{i\in I} \alpha_{i}.P_{i}$ is the terminated process, that cannot perform any action; this process will be represented with the symbol **0**.
+
+We shall usually omit tail occurrences of ‘.0’ and, for example, simply write a.b instead of a.b.0
+