This question investigates a variant of our standard TM model from class. Our standard model included a tape which was infinite in one direction only.
Consider now a TM whose tape is infinite in both directions (i.e. you can move left or right infinitely many spaces on the tape). We call this a TM with doubly infinite tape.
(a) Show that a TM with doubly infinite tape can simulate a standard TM.
(b) Show that a standard TM can simulate a TM with doubly infinite tape.
(c) What does this imply about the sets of languages recognized by both models?