GATE | GATE CS 1996 | Question 8

Which two of the following four regular expressions are equivalent? (ε is the empty string).
(i). (00)*(ε+0)
(ii). (00)*
(iii). 0*
(iv). 0(00)*
(A) (i) and (ii)
(B) (ii) and (iii)
(C) (i) and (iii)
(D) (iii) and (iv)

Answer: (C)
Explanation: Here,

(00)*(ε+0)
= (00)*.ε+ (00)*.0 
= (00)* + (00)*0 
= 0* 

It is equal to (iii) [ using regular expression properties ].

Here,
we see that (00)* generates strings of even length and (00)*0 generated the strings of odd length.

Option (C) is correct.
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