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The expression (a|b)* and the expression (a*b*)* denote

  • A.different languages, the first omitting the empty string
  • B.languages that cannot be compared by any known method
  • C.the same language, namely all strings over a and b
  • D.different languages, the second omitting some strings

Answer: C

Both generate every string over the two letters, including the empty one. This pair is the standard illustration that very differently written expressions can denote the same regular language. Only minimisation of the corresponding automata settles the question conclusively.

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