Let L denotes the language generated by the grammar S 0S000 Which of the following is true GATE CSE 2000

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Let L denotes the language generated by the grammar S -> 0S0/00. Which of the following is true? GATE CSE 2000

A=L = 0+
B=L is regular but not 0+
C=L is context free but not regular
D=L is not context free


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answer: (B) 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)+. DFA (00)+ (1) Option B : Hence This option is Correct, because L is Regular but not 0+, as we proved above.

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