The examples of nfa":bookofproofs$8502 give rise to the question, whether the class $\mathcal L(\operatorname{NFA})$ of all languages accepted by any NFA is bigger than the class $\mathcal L(\operatorname{DFA})$ of all languages accepted by any DFA, due to the non-determinism of the NFA, as compared to the determinism of the DFA.
This question has been answered by Michael Rabin (1931 - ) and Dana S. Scott (1932 - ) in 1959 in Finite Automata and Their Decision Problems.
For every non-deterministic finite automaton. NFA there is a deterministic finite automaton. DFA accepting the same language. In other words, the class $\mathcal L(\operatorname{NFA})$ of all languages accepted by any NFA equals the class $\mathcal L(\operatorname{DFA})$ of all languages accepted by any DFA, formally
$$\mathcal L(\operatorname{NFA})=\mathcal L(\operatorname{DFA}).$$
Proofs: 1