Which of the following statements is/are correct about the regular expression?…
2022
Which of the following statements is/are correct about the regular expression?
aa*bb*cc*dd*
A. The language is {a^n b^n c^m d^m | n >= 1, m >= 1} U {a^n b^m c^m d^n | n >= 1, m >= 1}.
B. The given CFG generates the language of the regular expression:
S -> AB | CA -> aAb | abB -> cBd | cdC -> aCd | aDdD -> bDc | bc
C. The expression requires equal numbers of a’s, b’s, c’s and d’s.
Choose the correct answer from the options given below:
- A.
None of A, B and C is correct
- B.
Only B is correct
- C.
Both A and B are correct
- D.
All the three A, B and C are correct
Attempted by 37 students.
Show answer & explanation
Correct answer: A
Correct answer: None of A, B and C is correct
The expression aa*bb*cc*dd* simplifies to a+ b+ c+ d+. So the actual language is {a^i b^j c^k d^l | i, j, k, l >= 1}, where the four counts are independent.
Statement A is false: it imposes equality between some counts, such as the number of a’s and b’s. A counterexample is
abbcd, which matches the regular expression but is not in A’s union language.Statement B is false: the grammar generates the same equal-count union pattern described in A, not the independent-count language
a+ b+ c+ d+.Statement C is false: the regular expression does not require equal counts across the four blocks.
Final answer: None of A, B and C is correct.
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