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 problems in TOC?

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 does it mean if a language is 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.

### Are undecidable problems solvable?

There are some problems that a computer can never solve, even the world’s most powerful computer with infinite time: the undecidable problems. 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**.

### Why is L halt undecidable?

A language L is **undecidable if L is not decidable**. Thus, there is no Turing machine M that halts on every input and L(M) = L. L is recursively enumerable but not decidable. … Thus, Ld is the collection of Turing machines (programs) M such that M does not halt and accept when given itself as input.

### What types of problems are undecidable?

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 problems are not computable?

(Undecidable simply means non-computable in the context of a decision problem, whose answer (or output) is either “true” or “false”). A non-computable is a problem for which there is no algorithm that can be used to solve it. Most famous example of a non-computablity (or undecidability) is the **Halting Problem**.

### 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 is the difference between decidable and undecidable problems?

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. On the other hand, how could we possibly establish (= prove) that some decision problem is undecidable?

### Is Fermat’s theorem undecidable?

So could Fermat’s last theorem be **undecidable** from the standard axioms of number theory. So it looks entirely possible that it is indeed undecidable. …

### What is the halting problem an example of?

The halting problem is an early example of **a decision problem**, and also a good example of the limits of determinism in computer science.

### Which problem is computable?

**A mathematical problem** is computable if it can be solved in principle by a computing device. Some common synonyms for “computable” are “solvable”, “decidable”, and “recursive”. Hilbert believed that all mathematical problems were solvable, but in the 1930’s Gödel, Turing, and Church showed that this is not the case.

### Is it possible for a problem to be in both P and NP?

Is it possible for a problem to be in both P and NP? **Yes**. Since P is a subset of NP, every problem in P is in both P and NP.

### How do you know if a function is computable?

To summarise, based on this view a function is computable if: (a) given an input from its domain, possibly relying on unbounded storage space, it can give the corresponding output by following a procedure (program, algorithm) that is formed by a **finite number of exact unambiguous instructions**; (b) it returns such …

### What are the consequences of the problem being Undecidable?

What are the implications of the problem being undecidable? **The problem may be solvable in some cases**, but there is no algorithm that will solve the problem in all cases. A programmer develops the procedure maxPairSum() to compute the sum of subsequent pairs in a list of numbers and return the maximum sum.

### How do you prove halting problems?

Theorem (Turing circa 1940): There is no program to solve the Halting Problem. Proof: **Assume to reach a contradiction that there exists a program Halt(P, I) that solves the halting problem**, Halt(P, I) returns True if and only P halts on I.

### What are unreasonable time algorithms?

An unreasonable time algorithm is **a problem that would take a massive amount of computing power to solve**. The amount of time it would take to calculate a solution would be unreasonable, hence the name.

### How do you prove 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.

### How do you prove Decidable?

To show that a language is decidable, we need **to create a Turing machine which will halt on any input string from the language’s alphabet**. Since M is a dfa, we already have the Turing Machine and just need to show that the dfa halts on every input.

### Is L accept recognizable?

Thus, L is **a Turing Recognizable Language** (since the TM M recognizes it).

### Which problem is undecidable Mcq?

Undecidable Problems MCQ Question 1 Detailed Solution

The decidability problem of Turing Machines can directly be determined using Rice’s theorem. L1 is undecidable. According to Rice’s theorem, **emptiness problem of Turing machine** is undecidable.

### Can every problem be solved with an algorithm?

Every problem can be solved with an algorithm **for all possible inputs**, in a reasonable amount of time, using a modern computer. … There exist problems that no algorithm will ever be able to solve for all possible inputs.