What does it mean when a problem is undecidable?

An undecidable problem is one that should give a “yes” or “no” answer, but yet no algorithm exists that can answer correctly on all inputs.

Why is the halting problem unsolvable?

But the halting problem is unsolvable, which means that it is impossible to test if an arbitrary Turing machine T halts on an arbitrary input x.

Are undecidable problems unsolvable?

An undecidable problem is one for which no algorithm can ever be written that will always give a correct true/false decision for every input value. Undecidable problems are a subcategory of unsolvable problems that include only problems that should have a yes/no answer (such as: does my code have a bug?).

What is halting problem in DAA?

In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever.

What do you mean by saying that the halting problem of TM is undecidable?

So the both condition is non halting for CM machine/program even we had assumed in the beginning that it would halt.So this is the contradiction and we can say that our assumption was wrong and this problem, i.e., halting problem is undecidable.

What is the halting problem can it be solved by a computer and if so how?

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.

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.

What type of problem is the halting problem?

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.

What is halting problem in data structure?

The Halting Problem is the problem of deciding or concluding based on a given arbitrary computer program and its input, whether that program will stop executing or run-in an infinite loop for the given input.

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.

How are undecidable problems similar to halting problems?

Quite a few of those, once simplified, look like another case of the halting problem. Generally, all the undecidable problems revolve around the difficulty of determining properties about the input and output of programs.

How to prove that La is an undecidable problem?

Proof by Contradiction and Construction Assume MBis a TM that decides LB. Do a construction using MBto build A, a TM that decides LA. Since LA is undecidable, MA cannot exist. We have reached a contradiction, so (as long as nothing else is questionable) our assumption must be wrong. This shows LA reduces to LB, proving LBis at least as hard as LA .

Is the halting problem on a computer decidable?

The halting problem on usual computers is also decidable. To see this, note that there are a finite number of bits in the memory, and thus a finite number of possible configurations the computer can be in. If a program ever repeats a configuration, it will never terminate.