GATE | GATE-CS-2009 | Question 14

Which one of the following languages over the alphabet {0,1} is described by the regular expression: (0+1)*0(0+1)*0(0+1)* ?
(A) The set of all strings containing the substring 00.
(B) The set of all strings containing at most two 0’s.
(C) The set of all strings containing at least two 0’s.
(D) The set of all strings that begin and end with either 0 or 1.


Answer: (C)

Explanation: The regular expression has two 0′s surrounded by (0+1)* which means accepted strings must have at least 2 0′s.

The least possible string is ε 0 ε 0 ε = 00

The set of strings accepted is = { 00, 000, 100, 0010, 0000, 00100, 1001001,…..}

We can see from the set of accepted strings that all of the have at least two zeros which is the least possible string.

So option (C) is correct.

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