GATE CS 2007 Q74 — Regular Expressions and Finite Automata

To find the regular expression accepted by the given Finite State Automaton, let us analyze the transitions between the states:

• Start State ($q_0$): There is a self-loop on input $b$. This means the automaton can read any number of $b$'s initially, represented by $b^*$.
• Transition to $q_1$: To move from the non-accepting start state $q_0$ to the accepting state $q_1$, the automaton must consume exactly one $a$.
• Accepting State ($q_1$): Once in $q_1$, there are self-loops for both $a$ and $b$. This allows any sequence of $a$'s and $b$'s to be accepted, represented by $(a+b)^*$.

Combining these parts sequentially, the regular expression for the language accepted by the automaton is:

Hence, the correct option is C.