Determine what the Turing machine in Example 9.7 does when presented with the inputs aba andaaabbbb.Is there any input for which the Turing machine in Example 9.7 goes into an infinite loop? Example 9.7For E = {a,b}, design a Turing machine that acceptsL= {a,b„:n21}.Intuitively, we solve the problem in the following fashion. Starting at the leftmost a, we check it offby replacing it with some symbol, say x. We then let the read-write head travel right to find theleftmost b, which in turn is checked off by replacing it with another symbol, say y. After that, we goleft again to the leftmost a, replace it with an x, then move to the leftmost band replace it with y, andso on. Traveling back and forth this way, we match each a with a corresponding b. If after some timeno a's or b's remain, then the string must be in L.Working out the details, we arrive at a complete solution for which Q= {qo91;9293,94},F= {q4},E= {a,b},T={a,b, x, y,¤}. The transitions can be broken into several parts. The set

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Determine what the Turing machine in Example 9.7 does when presented with the inputs aba and aaabbbb. Is there any input for which the Turing machine in Example 9.7 goes into an infinite loop?

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter10: Classes And Data Abstraction

Section: Chapter Questions

Problem 19PE

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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

Determine what the Turing machine in Example 9.7 does when presented with the inputs aba and
aaabbbb.
Is there any input for which the Turing machine in Example 9.7 goes into an infinite loop?

Example 9.7
For E = {a,b}, design a Turing machine that accepts
L= {a,b„:n21}.
Intuitively, we solve the problem in the following fashion. Starting at the leftmost a, we check it off
by replacing it with some symbol, say x. We then let the read-write head travel right to find the
leftmost b, which in turn is checked off by replacing it with another symbol, say y. After that, we go
left again to the leftmost a, replace it with an x, then move to the leftmost band replace it with y, and
so on. Traveling back and forth this way, we match each a with a corresponding b. If after some time
no a's or b's remain, then the string must be in L.
Working out the details, we arrive at a complete solution for which Q= {qo91;9293,94},F= {q4},
E= {a,b},T={a,b, x, y,¤}. The transitions can be broken into several parts. The set

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