So, in the construction of equivalent NFA N' without -transition from any NFA with moves. the first rule can now be written as

Equivalence of NFA and DFA

It is worth noting that a DFA is a special type of NFA and hence the class of languages accepted by DFA s is a subset of the class of languages accepted by NFA s. Surprisingly, these two classes are in fact equal. NFA s appeared to have more power than DFA s because of generality enjoyed in terms of -transition and multiple next states. But they are no more powerful than DFA s in terms of the languages they accept.

Converting DFA to NFA

Theorem: Every DFA has as equivalent NFA

Proof: A DFA is just a special type of an NFA . In a DFA , the transition functions is defined from whereas in case of an NFA it is defined from and be a DFA . We construct an equivalent NFA as follows.