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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
 
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-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
+