Which of the following is (are) correct about the regular expression?

aa*bb*cc*dd*

A. The language for the given expression is:

L = {anbncmdm | n ≥ 1, m ≥ 1} U {anbmcmdn | n ≥ 1, m ≥ 1}

B. The Context Free Language for the given expression is:

S → AB | C

A → aAb | ab

B → cBd | cd

C → aCd | aDd

D → bDc | bc

C. The language generated by this expression is equal number of 'a's, followed by equal number of 'b's, followed by equal number of 'c's and followed by equal number of 'd's.

Choose the correct answer from the options given below:

The correct answer is Both A and B are correct

Key Points

• Let's analyze the given regular expression and the options:
• The given regular expression is aa*bb*cc*dd*, where:
  • a* denotes zero or more occurrences of 'a'
  • b* denotes zero or more occurrences of 'b'
  • c* denotes zero or more occurrences of 'c'
  • d* denotes zero or more occurrences of 'd'
• Now, let's evaluate the options:
• A. The language for the given expression is:
  • \(L = \{a^n b^n c^m d^m \mid n \geq 1, m \geq 1\} \cup \{a^n b^m c^m d^n \mid n \geq 1, m \geq 1\}\)​
  • Example: abcd, aabcdd, ....
  • This is correct. The regular expression generates strings with an equal number of 'a's followed by an equal number of 'b's, and then an equal number of 'c's followed by an equal number of 'd's.
• B. The Context Free Language for the given expression is: 
  • ​\(\begin{align*} S &\to AB \mid C \\ A &\to aAb \mid ab \\ B &\to cBd \mid cd \\ C &\to aCd \mid aDd \\ D &\to bDc \mid bc \end{align*}\)
  • Example: abcd, aabcdd, ....
  • This is correct. The context-free grammar represents the same language as the regular expression.

So, the correct answer is: \(\text{3) Both A and B are correct} \)