Covert the regular expression (ab(a+c)) (Alphabet ={a, b, c}) to a state diagram following the steps and conditions below, also draw diagrams of sub-expressions and label:

Following these conditions (recursive algorithm):

1) exactly one final state that is not the start state, 2) the start state has no incoming transitions, 3) the final state has no outgoing transitions

Inductive steps:

for union: merge start state of 1st with start state of 2nd, merge final state of 1st with final state of 2nd

for concatenation: merge final state of 1st with start state of 2nd (merged state is not final)

for closure: merge start state of 1st and final state of 1st (merged state is not final or start), two new states (final and start)