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Consider the language consisting of Turing Machines that accept at least two different strings, X = {(M) | M is a Turing Machine that accepts at least two different inputs}. That is, (M) EX if and only if |L(M)| ≥ 2. 1. Show that X is Turing-recognizable. 2. Give a mapping reduction ATM ≤m X, and explain why it works. 3. What can we conclude about X from the fact that ATM ≤m X?

Consider the language consisting of Turing Machines that accept at least two different strings, X = {(M) | M is a Turing Machine that accepts at least two different inputs}. That is, (M) EX if and only if |L(M)| ≥ 2. 1. Show that X is Turing-recognizable. 2. Give a mapping reduction ATM ≤m X, and explain why it works. 3. What can we conclude about X from the fact that ATM ≤m X?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the language consisting of Turing Machines that accept at least two different strings, X = {(M) | M is a Turing Machine that accepts at least two different inputs}. That is, (M) EX if and only if |L(M)| ≥ 2. 1. Show that X is Turing-recognizable. 2. Give a mapping reduction ATM ≤m X, and explain why it works. 3. What can we conclude about X from the fact that ATM ≤m X?
Transcribed Image Text:Consider the language consisting of Turing Machines that accept at least two different strings, X = {(M) | M is a Turing Machine that accepts at least two different inputs}. That is, (M) EX if and only if |L(M)| ≥ 2. 1. Show that X is Turing-recognizable. 2. Give a mapping reduction ATM ≤m X, and explain why it works. 3. What can we conclude about X from the fact that ATM ≤m X?
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