1. (4 marks) Using the method described in Section 9.1 and in videos of Week 3 (video no. 12) convert the following regular expression into a state diagram: (ab*(a + c))* Here the alphabet is = {a,b,c}. Note that the closure operation has highest precedence so ab* denotes strings with one occurrence of a and zero or more occurrences of b. Your answer should indicate how you arrived at the result: As intermediate steps write down the state diagrams that you construct for subex- pressions of the given regular expression, and for each intermediate step clearly indicate which subexpression it corresponds to. Please do not simplify/modify the state diagrams. Simplifications/modifications of the state diagrams are considered as errors when marking (independently of whether or not the state diagram remains equivalent). Please note: The question is marked based on how well you follow the steps of the algorithm of section 9