22. (15 points). Your instructor dislikes Turing Machines and has come up with an alternative model. Like a TM it is a finite state machine with a single tape. This automaton, the Stansifer Machine, has four instructions: (a) SCAN a: if the symbol under the read head is a a, transition to the next state (b) WRITE a: unconditionally write the symbol a at the current position in the tape (and transition to the next state) (c) LEFT: (unconditionally) move left (d) RIGHT: (unconditionally) move right (a) Formalize the Stansifer Machine, (b) define an instantaneous description for it, and (c) define a reasonable notion of acceptance. Then, (d) prove that the Stansifer Machine is equivalent to a Turing Machine