Which of the following is equal Regular Expression for the given Finite…
2025
Which of the following is equal Regular Expression for the given Finite Automata?
- A.
(aa + bb) a* (ab + ba)
- B.
(aa + bb) (a + b)* (aa + bb)
- C.
a* (a + b)* ab
- D.
bb(a + b)* aa
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Correct answer: B
The automaton starts at state S1 and reaches state S4 via two paths: 'aa' through S2 or 'bb' through S3. This forms the prefix (aa + bb).
At state S4, there is a self-loop on inputs 'a' and 'b', which represents the Kleene star term (a + b)*.
From S4, paths lead to final states S6 and S8 via 'aa' or 'bb', forming the suffix (aa + bb).
Concatenating these parts gives the regular expression (aa + bb)(a + b)*(aa + bb).