What is the halting problem for Turing machine?

What is the halting problem for Turing machine?

The halting problem is a decision problem about properties of computer programs on a fixed Turing-complete model of computation, i.e., all programs that can be written in some given programming language that is general enough to be equivalent to a Turing machine.

How did Turing solve the halting problem?

In 1936, Alan Turing proved that the halting problem over Turing machines is undecidable using a Turing machine; that is, no Turing machine can decide correctly (terminate and produce the correct answer) for all possible program/input pairs. …

How does a Turing machine halt?

A Turing machine can either eventually enter an accepting state, enter a rejecting state, or loop forever. If it enters either an accepting or rejecting state, then it halts.

Do Turing machines always halt on all finite inputs?

Functions computable by total Turing machines A machine that uses only finite memory on any particular input can be forced to halt for every input by restricting its flow control capabilities so that no input will ever cause the machine to enter an infinite loop.

Can a human solve the halting problem?

Humans are “smart” because of smart algorithms that are cleverly written in neurons so computer scientists can’t steal or efficiently implement them. However clever these algorithms are, they most likely cannot reliably solve the halting problem.

Is halting problem solvable?

Because the halting problem is not solvable on a Turing machine, it is not solvable on any computer, or by any algorithm, given the Church-Turing thesis. Many other unsolvability results are derived starting from the ones given here.

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.

Can a Turing machine have infinite input?

A classic Turing Machine has an infinite tape with a finite input string. As such, while there is no limit to how long the input can be, it cannot be infinite. Having said that, there are many alternative machines that work similarly to a TM but with infinite input sequences.

What makes a problem Undecidable?

In computability theory, an undecidable problem is a type of computational problem that requires a yes/no answer, but where there cannot possibly be any computer program that always gives the correct answer; that is, any possible program would sometimes give the wrong answer or run forever without giving any answer.

Why is the halting problem Undecidable?

Example: the halting problem in computability theory 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.

What is the Halting State in a Turing machine?

The Halting problem refers to the question of whether someone can write a computer program that takes another program as input and check if this new program will stop after a finite number of CPU cycles or will run forever if the new program were to run on its own with its own input.

When did Alan Turing prove the halting problem?

Halting Problem. In 1936, Alan Turing proved that the halting problem over Turing machines is undecidable using a Turing machine; that is, no Turing machine can decide correctly (terminate and produce the correct answer) for all possible program/input pairs.

Can a Turing machine finish computing the string w?

Input − A Turing machine and an input string w. Problem − Does the Turing machine finish computing of the string w in a finite number of steps? The answer must be either yes or no.

Is the output of a halting machine always yes?

If the halting machine finishes in a finite amount of time, the output comes as ‘yes’, otherwise as ‘no’. The following is the block diagram of a Halting machine − If H returns YES, then loop forever. If H returns NO, then halt. The following is the block diagram of an ‘Inverted halting machine’ −