Exercise 2: Undecidahility 20 marks Let L1 = {M I AI is a TM that halts on the empty tape leaving exactly two words on its tape in the form Huh Bui2B}. (a) (15 marks) You have seen the proof in tutorial 7 (PART 2) that AT the problem of deciding whether an arbitrary Turing machine will accept an arbitrary input, is undecidable. Use this result to prove, formally using problem reduction, that given an arbitrary Turing machine _If, the problem of deciding if M E L1 is undecidable. (b) (5 marks) Is L1 recursive, recursively enumerable, non-recursively enumerable, uncomputable? Justify your answer. Exercise 3: Complexity 25 marks (a) (6 marks) Prove mathematically that if a Turing Machine runs in time 0(g(n)), then it runs in time 0(h (g(n))+ c), for any constant c > 0 and any functions g( it) and h(n) where h(n) > n. (b) (14 marks) A cutting•edge publisher based in Melbourne is publishing a book on complexity theory. They learnt that you are taking so they offered you a very well paid job! For the job, you arc asked to write the pan of the book that explains the following picture: