## 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 there a language for every Turing machine?

The TM will then either accept the string, reject the string, or loop on the machine. The language of a TM is defined as the set of all the strings it accepts. Not every language is the language of a Turing machine – that’s one of the landmark results of theoretical computer science.

Are Turing machines 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.

How do you show an undecidable language?

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.

### How many undecidable languages are there?

two undecidable languages
We’ve now proven the existence of two undecidable languages (ATM and ATM) and one unrecognizable language (ATM).

### What is decidable and undecidable languages?

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.

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 are undecidable problems about Turing machine?

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’.

#### What makes something 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.