Can an undecidable problem ever be solved?

Definition: A decision problem is a problem that requires a yes or no answer. Definition: A decision problem that admits no algorithmic solution is said to be undecidable. No undecidable problem can ever be solved by a computer or computer program of any kind.

Will the halting problem ever be solved?

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.

Why is the halting problem undecidable?

This is an undecidable problem because we cannot have an algorithm which will tell us whether a given program will halt or not in a generalized way i.e by having specific program/algorithm.In general we can’t always know that’s why we can’t have a general algorithm.

What is an example of an undecidable problem?

Examples – These are few important Undecidable Problems: As a CFG generates infinite strings, we can’t ever reach up to the last string and hence it is Undecidable. Whether two CFG L and M equal? Since we cannot determine all the strings of any CFG, we can predict that two CFG are equal or not.

How do you show an undecidable problem?

For a correct proof, need a convincing argument that the TM always eventually accepts or rejects any input. How can you prove a language is undecidable? To prove a language is undecidable, need to show there is no Turing Machine that can decide the language.

In what ways might a logic be undecidable?

First-order logic is not decidable in general; in particular, the set of logical validities in any signature that includes equality and at least one other predicate with two or more arguments is not decidable. Logical systems extending first-order logic, such as second-order logic and type theory, are also undecidable.

What does it mean for a problem to be 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.

How do you explain the halting problem?

unsolvable algorithmic problem is the halting problem, which states that no program can be written that can predict whether or not any other program halts after a finite number of steps. The unsolvability of the halting problem has immediate practical bearing on software development.

What is undecidable problem how can it be solved?

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.

What does it mean for a language to be undecidable?

(definition) Definition: A language for which the membership cannot be decided by an algorithm — equivalently, cannot be recognized by a Turing machine that halts for all inputs. See also decidable language, undecidable problem, decidable problem.

How can you prove that a language is undecidable?

Your language L is indeed undecidable. This can be shown by reducing the halting problem to L: For the halting problem instance (N, y), create a new machine M for the L problem. On input x, M simulates (N, y) for length(x) steps. If the simulation halted within that number of steps, then M halts.

What is the profound truth that the halting problem conveys?

A profound truth that the Halting problem conveys is that no matter how smart, powerful and intelligent you create an implementation of a Turing Machine, there will always be a class of problems you will never be able to solve. Give a function F and it’s input I, determine whether F halts when run on input I?

What is an undecidable problem in Computer Science?

In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is impossible to construct a single algorithm that always leads to a correct yes-or-no answer. A decision problem is any arbitrary yes-or-no question on an infinite set of inputs.

Is there any solution to a decision problem?

A decision problem has only two possible outputs (yes or no) on any input. In computability theory and computational complexity theory, a decision problem is a problem that can be posed as a yes-no question of the input values. Like is there any solution to a particular problem? The answer would be either a yes or no.

What is the unsolvability of halting problem?

The unsolvability of the halting problem means specifically that there is no Turing machinethat, when presented with the input of another Turing machine (in any reasonable description) and some input, will determine whether the input Turing machine will halt on the input string (and always output a yes or no answer in a finite amount of time).