Extended transition function :

Extend (which is function on symbols) to a function on strings, i.e. .

That is, is the state the automation reaches when it starts from the state q and finish processing the string w. Formally, we can give an inductive definition as follows:

The language of the DFA M is the set of strings that can take the start state to one of the accepting states i.e.

L(M) = { | M accepts w }

          = {| }