Which one of the following regular expressions correctly represents the language of the finite automaton given below?
Which one of the following regular expressions correctly represents the language of the finite automaton given below?
Show Hint
- \( ab^*bab^* + ba^*aba^* \)
- \( (ab^b)ab^+ + (ba^a)^*ba^* \)
- \( (ab^b + ba^a)(a^* + b^*) \)
- \( (ba^a + ab^b)^*(ab^b + ba^a) \)
The Correct Option is D
Solution and Explanation
- Option (A) correctly reflects the behavior of the automaton by allowing for the repetition of a and b in particular sequences.
- Option (D) also matches the structure of the transitions based on the automaton diagram.
Thus, the correct answer is (A) and (D).
Final Answer: (A) and (D)
Top Questions on Regular expressions and finite automata
Match LIST-I with LIST-II \[\begin{array}{|c|c|c|}\hline \text{ } & \text{LIST-I} & \text{LIST-II} \\ \hline \text{A.} & \text{A Language L can be accepted by a Finite Automata, if and only if, the set of equivalence classes of $L$ is finite.} & \text{III. Myhill-Nerode Theorem} \\ \hline \text{B.} & \text{For every finite automaton M = $(Q, \Sigma, q_0, A, \delta)$, the language L(M) is regular.} & \text{II. Regular Expression Equivalence} \\ \hline \text{C.} & \text{Let, X and Y be two regular expressions over $\Sigma$. If X does not contain null, then the equation $R = Y + RX$ in R, has a unique solution (i.e. one and only one solution) given by $R = YX^*$.} & \text{I. Arden's Theorem} \\ \hline \text{D.} & \text{The regular expressions X and Y are equivalent if the corresponding finite automata are equivalent.} & \text{IV. Kleen's Theorem} \\ \hline \end{array}\]
\[\text{Matching List-I with List-II}\]
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