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# GATE | GATE CS Mock 2018 | Set 2 | Question 26

Which of following statement(s) is/are not correct? (I) Languages generated by the grammar S→aSa ∣ aa is not regular. (II) Languages generated by the grammar S→aSb ∣ aa is not regular. (III) Languages generated by the grammar S→S1|S3, S1→aS1c |S2|λ, S2→aS2b|λ, S3→aS3b|S4| λ, S4→bS4c|λ is {a^nb^mc^k | k = |n – m|, n≥0, m≥0, k≥0}. (IV) Languages generated by the grammar S→S1S3, S1→aS1c |S2|λ, S2→aS2b|λ, S3→aS3b|S4| λ, S4→bS4c|λ is {a^nb^mc^k | k = |n – m|, n≥0, m≥0, k≥0}.

(A)

Only (II), (IV)

(B)

Only (I), (III), (IV)

(C)

Only (I), (II), (III)

(D)

All of the above

Answer: (B)

Explanation:

(I) Grammar S→aSa ∣ aa generates language (aa)+ which is regular. (II) Grammar S→aSb ∣ aa generates language a^n(aa)b^n which is not regular. (III) Production rule of S3 doesn\’t follow Language L, as it generates at least one word which is not in L: abcb. (IV) Grammar generates the word acab which is not in L Therefore, only statements (I), (III), (IV) are not correct. Option (B) is correct.

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