DFA

Discrete finite automata.

Recognize the same languages as regular grammars.

Minimization

It is possible algorithmically minimize a DFA to an equivalent one with the smallest possible number of states.

The minimum is unique up to renaming, so it is also a good canonical form.

Hopcroft (1971) in $O(n log n)$ .

Equivalent power to deterministic, proved with definition in 1959.

Interestingly, the same is not the case for:

push down automata, in which deterministic are less powerful than non-deterministic
omega automatons

Turing machines are also equivalent to NTMs, but the change alters the complexity of computations.

Look just like automaton, but with one of several rules for what it means to accept a finite input.

Non-deterministic is strictly more powerful than deterministic in this case.