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What is the halting problem an example of?
The halting problem is an early example of a decision problem, and also a good example of the limits of determinism in computer science.
Is the halting problem undecidable?
Alan Turing proved in 1936 that a general algorithm running on a Turing machine that solves the halting problem for all possible program-input pairs necessarily cannot exist. Hence, the halting problem is undecidable for Turing machines.
Is the halting problem in NP?
It is also easy to see that the halting problem is not in NP since all problems in NP are decidable in a finite number of operations, but the halting problem, in general, is undecidable.
How does the proof of the halting problem work?
This is a “proof by contradiction”, a reductio ad absurdum. (Latin phrases are always good in theory classes… as long as they make sense, of course.) This program H is just a program with two inputs: a string representing a program for some machine, and an input.
How to prove that the halting problem is undecidable?
This program H is just a program with two inputs: a string representing a program for some machine, and an input. For purposes of the proof, you simply assume the program H is correct: it simply will halt and accept if M accepts with w.
Which is an example of the halting problem?
The halting problem is a decision problem in computability theory. It asks, given a computer program and an input, will the program terminate or will it run forever? For example, consider the following Python program: 1 2 3x = input() while x: pass It reads the input, and if it’s not empty, the program will loop forever.
Is there a program that can solve the halting problem?
Halting problem is perhaps the most well-known problem that has been proven to be undecidable; that is, there is no program that can solve the halting problem for general enough computer programs. It’s important to specify what kind of computer programs we’re talking about.