Consider the finite automata given below :

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The language b accepted by this automata is given by the regular expression :

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  1. b* a b * a b * a b * 
  2. (a + b)* 
  3. b*a (a + b)*
  4. b* ab* ab*

Answer (Detailed Solution Below)

Option 1 : b* a b * a b * a b * 
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The correct answer is Option 1: b* a b * a b * a b *.

key-point-image Key Points
  • The regular expression b* a b * a b * a b * represents the language accepted by the given finite automata.
  • This regular expression can be broken down as follows:
    • b* matches zero or more occurrences of the character 'b'.
    • a matches a single occurrence of the character 'a'.
    • Repeating the pattern b* a three more times ensures that the sequence 'a' appears exactly three times, each possibly preceded by zero or more 'b's.
  • This pattern matches any string of 'b's followed by 'a', and this sequence is repeated three times.
additional-information-image Additional Information
  • The finite automata can be visualized as having states that transition between each other upon reading specific inputs (characters).
  • Understanding the structure of the automata and the transitions helps in deriving the correct regular expression that represents the language it accepts.
  • Finite automata are used in various fields such as text processing, compiler design, and network protocols to recognize patterns and validate input sequences.
  • Regular expressions are a powerful tool for describing patterns in strings and are widely used in search algorithms, text processing, and input validation.
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