30P Let A be a Turing-recognizable l... [FREE SOLUTION]

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Introduction to Theory of Computation

Michael Sipser

Computer Science

3rd Edition 路 458 pages

ISBN: 9781133187790

Chapter 4: 30P (page 212)

Let A be a Turing-recognizable language consisting of descriptions of Turing machines, ${(M_{1}), (M_{2}), . . .}$ , where everyM_iis a decider. Prove that some decidable languageDis not decided by any deciderM_iwhose description appears in A. (Hint: You may find it helpful to consider an enumerator for A.)

Short Answer

Expert verified

The decidable language D is given that is not decided by any decider M_i

Step by step solution

Explain Turing machine

A Turing machine uses mathematics to simulate a machine that runs on tape mechanically. Such a machine is able to read and write symbols on a tape one at a time using a tape head. A limited number of simple instructions decide the operation completely.

Prove that D is not decidable

There is an enumerator E that counts A since it is Turing-recognizable. Allow M_i to be the i^th output of E. Let all the possible strings be $s 1, s 2, s 3, 鈥�$ and so on. Construct a Turing Machine D as described below.

Reject if w does not belong to $\{0, 1\} *$ .Otherwise, for some particular i, w is equal to s_i. Then, use E to numerate till M_i. After that, run M_i on w. Reject if M_i accepts. Otherwise, accept.

Thus, D is different fromany deciderM_i and not in A.

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Short Answer

Step by step solution

Explain Turing machine

Prove that D is not decidable

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91影视

Let A be a Turing-recognizable language consisting of descriptions of Turing machines, {M1,M2,...}, where everyMiis a decider. Prove that some decidable languageDis not decided by any deciderMiwhose description appears in A. (Hint: You may find it helpful to consider an enumerator for A.)

Short Answer

Step by step solution

Explain Turing machine

Prove that D is not decidable

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Databases

Blockchain Technology

Computer Organisation and Architecture

Problem Solving Techniques

Computer Programming

Cloud Services

Study anywhere. Anytime. Across all devices.