Consider the following Finite Automata. Which of the following is not a…

2025

Consider the following Finite Automata. Which of the following is not a Regular Expression for it?

  1. A.

    (a + b)* a

  2. B.

    b* a(a + bb* a)*

  3. C.

    b* ab*(ab*ab*)*

  4. D.

    (b + aa*b)* aa*

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Correct answer: C

The Finite Automata accepts strings that end in state q1, which requires the last symbol to be 'a'. Option C (b* ab*(ab*ab*)*) is incorrect because its structure allows the string to end in state q0. The initial segment b* a b* transitions from the start state back to itself, and the loop (ab* ab*)* also cycles between q0 and returns to q0. Consequently, this expression generates strings ending in 'b', not 'a'. In contrast, Options A, B, and D all ensure the final transition lands on q1. For instance, Option A (a + b)* a explicitly ends with 'a', and Option D (b + aa*b)* aa* ensures the last part is 'aa*', which also ends in 'a'. Therefore, Option C fails to describe the language accepted by the automaton.

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