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GATE | GATE-CS-2006 | Question 34

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Consider the regular language L = (111 + 11111)*. The minimum number of states in any DFA accepting this languages is:

(A)

3

(B)

5

(C)

8

(D)

9



Answer: (D)

Explanation:

The finite state automata is :                       

 

 Explanation: It is given that language L = (111 + 11111)* Strings , that belongs in the language are L = {null , 111 , 11111, 111111 , 11111111 , 111111111 , 1111111111 , ……. form string length 8 , (number of 1’s) , now we can can generate any length of string from length 3 and 5 (i.e. length 8 ,length 9, length 10 , length 11 ,…etc)} L = {null , 111 , 11111, 111111 , 11111111 , 111111111* } Strings in length , that belongs in the language L = {0 ,3, 5, 6, 8, 9, 10, 11, …} So, there are 5 states that are final states and 4 states that are non-final states Therefore total number of states are 9 states . hence option D is true. This explanation has been contributed by Namita Singh.


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Last Updated : 14 Feb, 2018
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