# What is undecidable language in Turing machine?

## What is undecidable language in Turing machine?

For an undecidable language, there is no Turing Machine which accepts the language and makes a decision for every input string w (TM can make decision for some input string though). A decision problem P is called “undecidable” if the language L of all yes instances to P is not decidable.

## Is an undecidable language Turing recognizable?

Every unrecognizable language is undecidable, but there are undecidable languages which are recognizable. In fact, the decidable languages are exactly those which are recognizable and co-recognizable (that is, have recognizable complement).

What is an undecidable algorithm?

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 decidable and undecidable language?

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.

### What is the definition of undecidable?

Definition of undecidable : not capable of being decided : not decidable … a huge popular audience, most of whom must have been baffled and exasperated by its elaborate and undecidable mystifications.—

### Are undecidable languages closed under complement?

– Decidable languages are closed under complementation. To design a machine for the complement of a language L, we can simulate the machine for L on an input. If it accepts then accept and vice versa. – Turing recognizable languages are not closed under complement.

Why Turing machine is undecidable?

Undecidable Problems A problem is undecidable if there is no Turing machine which will always halt in finite amount of time to give answer as ‘yes’ or ‘no’. An undecidable problem has no algorithm to determine the answer for a given input.

What problem is undecidable?

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’.

## How do you prove a language 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.

## Is the union of two undecidable languages decidable?

If L is the union of two regular languages, then its complement L is regular. If L is the union of two regular languages, then its complement L is context-free. If L is the union of two decidable languages, then L is decidable. If L is the union of two undecidable languages, then L is undecidable.

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