Construct a deterministic two-tape Turing machine, which begins with a string of the form anon the first tape, and a string of the form amon 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, in similar detail to that in Question 2, or others we have seen in class. Then draw a transition diagram for the machine. To earn full points for this question, your machine should handle the cases when either n or m is zero correctly. If it does not (but deals with all non-zero inputs correctly), you will still earn a majority of points for this question.

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Construct a deterministic two-tape Turing machine, which begins with a string of the form
anon the first tape, and a string of the form amon 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, in similar detail to that in Question 2, or others we
have seen in class.
Then draw a transition diagram for the machine.
To earn full points for this question, your machine should handle the cases when either n or m is zero
correctly. If it does not (but deals with all non-zero inputs correctly), you will still earn a majority of points
for this question.

Question 3. Construct a deterministic two-tape Turing machine, which begins with a string of the form
a" on the first tape, and a string of the form a" on the second tape. (n, mE 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, in similar detail to that in Question 2, or others we
have seen in class.
Then draw a transition diagram for the machine.
To earn full points for this question, your machine should handle the cases when either n or m is zero
correctly. If it does not (but deals with all non-zero inputs correctly), you will still earn a majority of points
for this question.
Transcribed Image Text:Question 3. Construct a deterministic two-tape Turing machine, which begins with a string of the form a" on the first tape, and a string of the form a" on the second tape. (n, mE 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, in similar detail to that in Question 2, or others we have seen in class. Then draw a transition diagram for the machine. To earn full points for this question, your machine should handle the cases when either n or m is zero correctly. If it does not (but deals with all non-zero inputs correctly), you will still earn a majority of points for this question.
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