Which of these strings can be represented by the regular expression: a*bb*abaaaa*?

The correct answer is Option 4: babaaaaaaa.

Key Points

• The regular expression a*bb*abaaaa* represents strings that follow these rules:
  • a*: Matches zero or more occurrences of the character 'a'.
  • bb*: Matches one 'b' followed by zero or more occurrences of 'b'.
  • ab: Matches the exact sequence 'ab'.
  • aaaa*: Matches 'aaaa' followed by zero or more occurrences of 'a'.
• Let's analyze each option:
  • Option 1: aaaabbbbbb - This string does not contain 'ab', so it does not match the regular expression.
  • Option 2: bbbbbbaaaa - This string does not contain 'ab', so it does not match the regular expression.
  • Option 3: aaaabaaaaa - This string does not contain 'ab', so it does not match the regular expression.
  • Option 4: babaaaaaaa - This string matches the regular expression:
    • a*: Matches zero occurrences of 'a'.
    • bb*: Matches one 'b'.
    • ab: Matches the sequence 'ab'.
    • aaaa*: Matches 'aaaa' followed by four 'a's.

Additional Information

• Regular expressions are used to define patterns for matching strings.
• They are commonly used in programming for searching, replacing, and validating text.
• The expression a*bb*abaaaa* ensures a specific sequence of characters while allowing flexibility with repetitions.
• Understanding the structure of a regular expression is crucial for determining valid matches.