Definition (Oracle Turing Machine). Let fo : {0,1}. {0,1} be a decision function

Question

Definition (Oracle Turing Machine). Let fo : {0,1}. {0,1} be a decision function. Say that a Turing Machine M* is enhanced with oracle access to fo if: 1. M* it has two extra tapes, the "fo-input" and "fo-output" tapes; and 2. during each time step, M* is allowed to "apply fo", in which case M writes fo(x) on the fo-output tape where x E 10, 1* is the string written on the fo-input tape. Problem 2. Let f, fo : {0,1}* {0, 1) and T.To : N N be decision and time functions. Suppose that a Turing Machine M which is enhanced with oracle access to fo computes f in time T. Suppose, furthermore, that a standard Turing Machine Mo computes fo in time To Construct a standard Turing Machine M (with as many tapes as you like) which computes f in time T . To

Explanation / Answer

Describe a TM that recognizes the language = "On input string : 1. Sweep left to right across the tape crossing off every other 2. If in stage 1 tape contained a single , accept 3. If in stage 1 tape contained more that a single and the number of s was odd, reject 4. Return the head to the left-hand of the tape 5. Go to stage 1"

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