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 a™ 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.

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 a™ 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.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Problems on Turing Machines

In the computational world, the Turing machine is a powerful computation engine. The invention of the Turing Machine is done by Alan Turing in 1936. A Turing Machine (TM) is a diagrammatic model of a fictional computer. It determines an output from a set of input variables using a pre-defined set of rules. It is used to get around the limitations of finite automata and pushdown automata.

Question

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 a" 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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