GATE | GATE-CS-2000 | Question 5

Let L denotes the language generated by the grammar S -> 0S0/00. Which of the following is true?
(A) L = 0+
(B) L is regular but not 0+
(C) L is context free but not regular
(D) L is not context free


Answer: (B)

Explanation: Option A : L is not 0+ , because 0+ will contain any arbitrary string over alphabet 0 with any no of 0’s ( except empty string ), for ex: {0, 00, 000,00000}, but L will only have the strings as { 00, 0000, 000000,…}, i.e only even no of  0’s ( excluding empty string}.

Option D : L is a Context Free Language, because the Grammar G which generates the language L is Context Free Grammar. A Grammar G is CFG if all of its productions are of the form A->α, where A is a single non-terminal and α belongs to (V∪ T)* , i.e  α can be a string of terminals and/or Non-terminals. (V represents a non-terminal and T represents a terminal)

Option C : L is a Regular Language, Because we are able to write a regular expression for it ( and also able to make a Finite Automaton), which is (00)+.

Option B :  Hence This option is Correct, because L is Regular but not 0+, as we proved above.

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