MCQ IN COMPUTER SCIENCE & ENGINEERING

COMPUTER SCIENCE AND ENGINEERING

THEORY OF COMPUTATION

Question [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
If NFA of 7 states is converted into DFA, maximum possible number of states for the DFA is?
A
64
B
132
C
128
D
127
Explanation: 

Detailed explanation-1: -We have four state which is not finale so all these state which come together to form a state in dfa are not have any finale state in dfa. so possible dfa state with only these 4 states is 24 = 16 and total number of state is 27 = 128 so total number of state which contain final state is 128-16 =112.

Detailed explanation-2: -For an arbitrary NFA with N states, the maximum number of states in an equivalent minimized DFA is 2N.

Detailed explanation-3: -So, the maximum number of states in the equivalent DFA of an NFA, will be 2n, where n is the number of states in NFA, as a set with n items has maximum 2n subsets.

Detailed explanation-4: -The maximum number of states is 2n. Conversion from NFA to DFA is done by subset construction and the number of states of the resulting DFA is in the worst case 2n.

Detailed explanation-5: -Answers. The maximum number of final states for a DFA can be total number of states itself and minimum would always be 1, as no DFA exits without a final state. Therefore, the solution is n+1.

There is 1 question to complete.