Can we have more than one Deterministic Finite Automata diagrams for a set of strings? Much like many math equations can be simplified. I am wondering if Deterministic Finite Automata diagrams can equal each other while some may be more simplified than others. I am following the youtube video and I am wondering if the graph that I drew with pencil and paper would also be correct. Given the Prompt:

Construct a DFA that accepts any strings over {a,b} that does not contain the string aabb in it.
Can we have more than one Deterministic Finite Automata (DFA) diagrams for a set of strings?


Of course!

There's also an algorithm to minimize a deterministic finite automata into a minimal deterministic finite automata. The existence of such algorithm is a proof that for most, if not all, sets of strings, many DFAs can be defined.