Question 1: Equivalent models of Turing Machines A RAM Turing Machine has the following tapes: Input tape Work tape RAM address tape The input tape is read-only. The rest are both read and write. There are two special instructions (ie, states) that a RAM Turing Machine has, in addition to a standard Turing Machine. Read from memory: The content the work tape, at the address given in the RAM address tape, is read and written in the current head location on the work tape. Write to memory: the content of the work tape, at the address given in the address tape, is rewritten to be the content under the current head location on the work tape. Both operations do not change the location of the head in the work tape. (a) Show that a standard TM (with a read-only input tape, and a read-write work tape) can simulate a RAM TM. (b) If the time complexity in the RAM TM is T(n), what is the time complexity of its simulation in the standard TM ? prove your answer. Hint: Mimic the structure of the proof that the number of tapes doesn't matter