NPTEL IIT Guwahati

Besides this the initial state of the DFA D has to be modified to keep track of all the states that can be reached from the initial state of NFA on zero or more -transitions. This can be done by changing the initial state to -closure ( ) .

It is clear that, at every step in the processing of an input string by the DFA D , it enters a state that corresponds to the subset of states that the NFA N could be in at that particular point. This has been proved in the constructions of an equivalent NFA for any -NFA

If the number of states in the NFA is n , then there are states in the DFA . That is, each state in the DFA is a subset of state of the NFA .

But, it is important to note that most of these states are inaccessible from the start state and hence can be removed from the DFA without changing the accepted language. Thus, in fact, the number of states in the equivalent DFA would be much less than .

Example : Consider the NFA given below.


	Removing Transition	Print this page
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	Besides this the initial state of the DFA D has to be modified to keep track of all the states that can be reached from the initial state of NFA on zero or more -transitions. This can be done by changing the initial state to -closure ( ) . It is clear that, at every step in the processing of an input string by the DFA D , it enters a state that corresponds to the subset of states that the NFA N could be in at that particular point. This has been proved in the constructions of an equivalent NFA for any -NFA If the number of states in the NFA is n , then there are states in the DFA . That is, each state in the DFA is a subset of state of the NFA . But, it is important to note that most of these states are inaccessible from the start state and hence can be removed from the DFA without changing the accepted language. Thus, in fact, the number of states in the equivalent DFA would be much less than . Example : Consider the NFA given below.
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