[3 marks] Show that f(n) = 7 + n Inn is (m2) for all integers n > 1 . Let A be the finite-state automaton with sets of finite states S =(S, S, S) and input values != {0 ,1) The states S1 and Ss are its initial and accepting states, respectively. The next-state function is given as follows. Next state State 0 Si S3 Construct the state-transition diagram for the automaton A. [1 mark i) Give a bit string of length four that is accepted by A. Give a bit string of [1 mark length four that is not accepted by A se regular expression to express the language that is accepted by the [1 mark] automaton A. d) Given the following graph: BE BE AC AC FAC c. ACF Use the breath first search algorithm to find a spanning 'tree in the above graph. Assume vertex B is the root and the vertices are ordered alphabetically. Show clearly each step of how the algorithm is performed and present your answer in a table with three columns, the first column is the number of steps, the second column is the queue for the search algorithm and the third column is the edges of the resulting spanning tree. S marks]