Given any NFA we need to construct as equivalent DFA i.e. the DFA need to simulate the behaviour of the NFA . For this, the DFA have to keep track of all the states where the NFA could be in at every step during processing a given input string.

There are possible subsets of states for any NFA with n states. Every subset corresponds to one of the possibilities that the equivalent DFA must keep track of. Thus, the equivalent DFA will have states.

The formal constructions of an equivalent DFA for any NFA is given below. We first consider an NFA without transitions and then we incorporate the affects of transitions later.

Formal construction of an equivalent DFA for a given NFA without transitions.

Given an without - moves, we construct an equivalent DFA

as follows

i.e.