## What would happen if the P vs NP problem was solved?

If P equals NP, **every NP problem would contain a hidden shortcut, allowing computers to quickly find perfect solutions to them**. But if P does not equal NP, then no such shortcuts exist, and computers’ problem-solving powers will remain fundamentally and permanently limited.

## Can P vs NP be solved?

Although one-way functions have never been formally proven to exist, most mathematicians believe that they do, and a proof of their existence would be a much stronger statement than P ≠ NP. Thus **it is unlikely that natural proofs alone can resolve P = NP**.

## What is the implication of finding a proof that P NP?

A proof would involve finding a polynomial time algorithm for an NP-complete problem. And when you find one polynomial algorithm, **you can use it to solve all other NP-complete problems by reducing the problems to a common form**. This means that a proof for P=NP and algorithms that use it will appear at the same time.

## What is the P versus NP problem what happens if P NP How would this affect computing problems as we currently know them?

Roughly speaking, P is a set of relatively easy problems, and NP is a set that includes what seem to be very, very hard problems, so **P = NP would imply that the apparently hard problems actually have relatively easy solutions**.

## Can NP problems be solved in polynomial time?

NP stands for Non-deterministic Polynomial time. This means that **the problem can be solved in Polynomial time using a Non-deterministic Turing machine** (like a regular Turing machine but also including a non-deterministic “choice” function).

## Can NP-hard problems be solved in polynomial time?

Consequences. **If P ≠ NP, then NP-hard problems could not be solved in polynomial time**. Some NP-hard optimization problems can be polynomial-time approximated up to some constant approximation ratio (in particular, those in APX) or even up to any approximation ratio (those in PTAS or FPTAS).

## What is P vs NP problem Justify your answer include definitions of P and NP class?

P versus NP

**It is not known whether P = NP**. However, many problems are known in NP with the property that if they belong to P, then it can be proved that P = NP. If P ≠ NP, there are problems in NP that are neither in P nor in NP-Complete. The problem belongs to class P if it’s easy to find a solution for the problem.

## What is the class of decision problems that can be solved by non-deterministic polynomial algorithm?

4. _________ is the class of decision problems that can be solved by non-deterministic polynomial algorithms. Explanation: **NP problems** are called as non-deterministic polynomial problems. They are a class of decision problems that can be solved using NP algorithms.

## Can you explain P NP NP completeness & NP-hard briefly?

Problems of NP can be verified by a Turing machine in polynomial time.

Types of Complexity Classes | P, NP, CoNP, NP hard and NP complete.

Complexity Class | Characteristic feature |
---|---|

NP-hard | All NP-hard problems are not in NP and it takes a long time to check them. |

NP-complete | A problem that is NP and NP-hard is NP-complete. |

## What is P problem what is NP problem and NP complete problem?

P is **a set of problems that can be solved by a deterministic Turing machine in Polynomial time**. NP is set of decision problems that can be solved by a Non-deterministic Turing Machine in Polynomial time.

## What is the relationship between the classes P and NP explain?

NP is set of problems that can be solved by a Non-deterministic Turing Machine in Polynomial time. P is subset of NP (any problem that can be solved by deterministic machine in polynomial time can also be solved by non-deterministic machine in polynomial time) but **P≠NP**.

## What is the relationship between P NP and NP-complete problems?

Difference between NP-Hard and NP-Complete:

NP-hard | NP-Complete |
---|---|

NP-Hard problems(say X) can be solved if and only if there is a NP-Complete problem(say Y) that can be reducible into X in polynomial time. | NP-Complete problems can be solved by a non-deterministic Algorithm/Turing Machine in polynomial time. |

## What is the relationship among P NP NP-complete and NP-hard problems?

All other problems in class NP can be reduced to problem p in polynomial time. **NP-hard problems are partly similar but more difficult problems than NP complete problems**. They don’t themselves belong to class NP (or if they do, nobody has invented it, yet), but all problems in class NP can be reduced to them.