Nondeterministic Finite Automaton - Equivalence To DFA

Equivalence To DFA

For each NFA, there is a DFA such that both recognize the same formal language. The DFA can be constructed using the powerset construction. It is important in theory because it establishes that NFAs, despite their additional flexibility, are unable to recognize any language that cannot be recognized by some DFA. It is also important in practice for converting easier-to-construct NFAs into more efficiently executable DFAs. However, if the NFA has n states, the resulting DFA may have up to 2n states, an exponentially larger number, which sometimes makes the construction impractical for large NFAs.