2. (Eco-friendly TM) An eco-friendly Turing machine (ETM) is the same as an ordinary (determin- istic) one-tape Turing machine, but it can read and write on both sides of each tape square: front and back. At the end of each computation step, the head of the eco-friendly TM can move left (L), move right (R), or flip to the other side of the tape (F). (a) Give a formal definition of the syntax of the transition function of an eco-friendly TM. (Modify Part 4 of Definition 3.3 on page 168 of the textbook.) (b) Show that eco-friendly TMs recognize the class of Turing-recognizable languages. That is, use a simulation argument to show that they have exactly the same power as ordinary TMs