(c) Let A be the finite-state automaton with states S = {s, S2,S3,S4} and input values 1 = {a,b}. The initial state is s, and the accepting state is {sg}. The next state function is give as follows State Next state b a S2 $ S2 Sz Sz $4 $ $4 S4 S2 (i) (ii) Construct the state-transition diagram for the automaton A. [1.5 marks] Determine whether the input " babbba" is accepted by the automaton. Show detail state transitions and justify your finding. [1.5 marks] Use regular expression to describe the language accepted by the automaton. [1 mark] (ii)