Construct a deterministic two-tape Turing machine, which begins with a string of the form an on the first tape, and a string of the form am on the second tape. (n, m ∈ N.) Both heads begin scanning the left-most character of each string. The Turing machine should accept if the number n is an integer multiple of the number m; i.e. there is some integer k such that n = k · m. First, describe the algorithm that your machine uses. Then draw a transition diagram for the machine. To answer properly, your machine should handle the cases when either n or m is zero correctly.

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Construct a deterministic two-tape Turing machine, which begins with a string of the form an on the first tape, and a string of the form am on the second tape. (n, m ∈ N.) Both heads begin scanning the left-most character of each string. The Turing machine should accept if the number n is an integer multiple of the number m; i.e. there is some integer k such that n = k · m.

First, describe the algorithm that your machine uses. Then draw a transition diagram for the machine. To answer properly, your machine should handle the cases when either n or m is zero correctly.

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