Now, given any NFA with -transition, we can first construct an equivalent NFA without -transition and then use the above construction process to construct an equivalent DFA , thus, proving the equivalence of NFA s and DFA s..

It is also possible to construct an equivalent DFA directly from any given NFA with -transition by integrating the concept of -closure in the above construction.

Recall that, for any

- closure :

In the equivalent DFA , at every step, we need to modify the transition functions to keep track of all the states where the NFA can go on -transitions. This is done by replacing by -closure , i.e. we now compute at every step as follows: