Using the method described in Section $9\mathrm{.}1($and in class$)$ convert the following regular expression into a state diagram:

$(a{b}^{*}(a+c){)}^{*}$

Here the alphabet is $=\{a,b,c\}.$ Note that the closure operation has highest precedence so $a{b}^{*}$ 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 $9\mathrm{.}1.$ Please include diagrams when answering