What are decidable and undecidable problems?

What are decidable and undecidable problems?

A decision problem P is undecidable if the language L of all yes instances to P is not decidable. An undecidable language may be partially decidable but not decidable. Suppose, if a language is not even partially decidable, then there is no Turing machine that exists for the respective language.

Which problems are decidable?

Definition: A decision problem that can be solved by an algorithm that halts on all inputs in a finite number of steps. The associated language is called a decidable language. Also known as totally decidable problem, algorithmically solvable, recursively solvable.

What do you understand by undecidable problem?

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.

What is the difference between decidable and undecidable TM?

A decision problem is decidable if there exists a decision algorithm for it. Otherwise it is undecidable. To show that a decision problem is decidable it is sufficient to give an algorithm for it.

How do you know if a language is decidable or undecidable?

A language is called Decidable or Recursive if there is a Turing machine which accepts and halts on every input string w. Every decidable language is Turing-Acceptable. A decision problem P is decidable if the language L of all yes instances to P is decidable.

What is the difference between undecidable problems and unreasonable time algorithms?

The difference between undecidable problems and unreasonable time algorithms is that an undecidable problem is a problem that no algorithm can be made this is always capable of providing a yes or no answer, while an unreasonable time algorithm is an algorithm with exponential efficiencies and cannot create an answer in …

How do you show a problem is decidable?

By definition, a language is decidable if there exists a Turing machine that accepts it, that is, halts on all inputs, and answers “Yes” on words in the language, “No” on words not in the language. Therefore one way of showing that a language is decidable is by describing a Turing machine that accepts it.

How is Reducibility is used to show problems is decidable or undecidable briefly explain?

Reducibility involves two problems A and B. When A is reducible to B solving A can not be “harder” than solving B. If A is reducible to B and B is decidable, then A is also decidable. If A is undecidable and reducible to B, then B is undecidable.

How do you prove that a problem is undecidable?

An algorithm for solving B could be used as a subroutine for solving A. If B is decidable, then A is decidable. (If there is an algorithm to solve B, then there is an algorithm to solve A.) We could prove that this problem is as hard as the halting problem; hence it is undecidable.

How do you show a problem is undecidable?

If CONST = TOTALP, then TOTALP outputs Yes for all inputs, which implies that P(x) halts on all inputs, which implies that P(x) is total. Thus, if we can determine whether CONST = TOTALP, we can solve the totality problem. Therefore, the equivalence problem is undecidable.

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?).

Why is the halting problem Undecidable?

The Halting Problem is Undecidable: Proof Since there are no assumptions about the type of inputs we expect, the input D to a program P could itself be a program. Compilers and editors both take programs as inputs.

How do you prove a problem is decidable?

To prove a language is decidable, we can show how to construct a TM that decides it. For a correct proof, need a convincing argument that the TM always eventually accepts or rejects any input.

How do you determine if a language is decidable or undecidable?

Can undecidable problem be solved?

Undecidable means “there is no algorithm that can solve all instances and that always terminates”.

How do you prove a problem is undecidable?

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. This is hard: requires reasoning about all possible TMs.

What is an undecidable problem how is it different from a reducible problem?

The problems for which we can’t construct an algorithm that can answer the problem correctly in the infinite time are termed as Undecidable Problems in the theory of computation (TOC). A problem is undecidable if there is no Turing machine that will always halt an infinite amount of time to answer as ‘yes’ or ‘no’.