Question

Regular expression for all strings starting with “ab” and ending with “ba” is:

• A. \( aba^* b^* ba \)
• B. \( ab(ab)^* ba \)
• C. \( ab(a + b)^* ba \)
• D. \( abba \)

Hint:

Regular expressions help define patterns in string matching.
- \( a^* \) means "zero or more occurrences of a".
- \( (a + b)^* \) means "zero or more occurrences of either 'a' or 'b'".
- Ensure the pattern correctly starts and ends with required substrings.

Answer 1

The Correct Option is C

Step 1: Understanding Regular Expressions A regular expression defines a pattern for strings that belong to a specific language. In this case, the required strings must:
- Start with "ab"
- End with "ba"
- Contain any combination of "a" and "b" in between.
Step 2: Evaluating the Given Options
- Option (A) \( aba^* b^* ba \): This restricts intermediate characters to specific repetitions of 'a' and 'b'.
- Option (B) \( ab(ab)^* ba \): This forces the intermediate characters to be repetitions of "ab", which is too restrictive.
- Option (C) \( ab(a + b)^* ba \): Allows any sequence of 'a' and 'b' between "ab" and "ba", making it the correct choice.
- Option (D) \( abba \): This only allows one specific string and does not generalize to all valid strings.
Step 3: Conclusion Since \( ab(a + b)^* ba \) correctly captures all possible strings satisfying the given conditions, option (C) is the correct answer.