Consider the problem of determining if a program P has any fixed points. Given any program...
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Consider the problem of determining if a program P has any fixed points. Given any program P, a fixed point is an input x such that P(x) outputs x. (a) Prove that the problem of determining whether a program has a fixed point is uncomputable. (b) Consider the problem of outputting a fixed point of a program if it has one, and outputting "Null" otherwise. Prove that this problem is uncomputable. (c) Consider the problem of outputting a fixed point of a program F if the fixed point exists and is a natural number, and outputting "Null" otherwise. Show that if this problem can be solved, then the problem in part (b) can be solved. What does this say about the computability of this problem? (You may assume that the set of all possible inputs to a program is countable, as is the case on your computer.) Consider the problem of determining if a program P has any fixed points. Given any program P, a fixed point is an input x such that P(x) outputs x. (a) Prove that the problem of determining whether a program has a fixed point is uncomputable. (b) Consider the problem of outputting a fixed point of a program if it has one, and outputting "Null" otherwise. Prove that this problem is uncomputable. (c) Consider the problem of outputting a fixed point of a program F if the fixed point exists and is a natural number, and outputting "Null" otherwise. Show that if this problem can be solved, then the problem in part (b) can be solved. What does this say about the computability of this problem? (You may assume that the set of all possible inputs to a program is countable, as is the case on your computer.)
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Lets consider each part of the problem a To prove that the problem of determining whether a program has a fixed point is uncomputable we can use a dia... View the full answer
Related Book For
Smith and Roberson Business Law
ISBN: 978-0538473637
15th Edition
Authors: Richard A. Mann, Barry S. Roberts
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