## What is undecidable problem in TOC?

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 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.

**What is undecidable problem in automata theory?**

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.

**What is undecidable problem how it can 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.

### Why do undecidable problems exist?

Created by Pamela Fox. Some problems take a very long time to solve, so we use algorithms that give approximate solutions. 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.

### 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?).

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

**When a problem is said to be Undecidable give an example of an Decidable problem?**

Give an example of undecidable problem? algorithm that takes as input an instance of the problem and determines whether the answer to that instance is “yes” or “no”. (eg) of undecidable problems are (1)Halting problem of the TM.

#### When a problem is said to be undecidable give an example of an Decidable problem?

#### How do you know if 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.

**Is the pumping lemma decidable for context free languages?**

Decision Problems for Context-Free Languages Based on the Pumping Lemma, we can state some decidability results for context-free languages. Lemma:It is decidable whether or not a given string belongs to a context-free language. Proof:

**Is it decidable if a context free language is empty?**

Lemma:It is decidable whether or not a context-free language is empty. Proof: We need to show that the corresponding context-free grammar can generate a string. If a CFG can generate a string, then it should be able to do so without using recursion (since we could just skip the recursion and generate a shorter string).

## Is the complement of a context free language recursive?

Note that trying to use “complementation” to solve (a) will not work, because the complement of a context-free language is not necessarily context free. In fact, the following proof effectively shows that the complement of a context-free language may not even be recursive (i.e. decidable by a TM).