# What is considered polynomial time?

## What is considered polynomial time?

A polynomial-time algorithm is an algorithm whose execution time is either given by a polynomial on the size of the input, or can be bounded by such a polynomial. Problems that can be solved by a polynomial-time algorithm are called tractable problems. Sorting algorithms usually require either O(n log n) or O(n2) time.

## What happens if P vs NP is solved?

If P=NP, then all of the NP problems can be solved deterministically in Polynomial time. If you could solve clique with a polynomial time algorithm, this would prove that P=NP, and then you could also use your method for solving clique to solve all of the other problems on that wiki-list, as an implication.

## Why do researchers believe P is not equal to NP?

intuitively P≠NP states that no matter how brilliantly creative the algorithm designer is, there are fundamental limits in improving the efficiency of code. in this way it even has parallels to physical laws eg thermodynamics.

## Is PA a subset of NP?

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). Therefore, NP-Complete set is also a subset of NP-Hard set.

## Why is P vs NP important?

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.

## What is NP full form?

NP means “No Problem.” The abbreviation NP is widely used in text-based messaging with the meaning “No Problem.” NP is typically used as a positive response to a request (i.e., to say “Yes”) and as a response to someone saying thank you (i.e., to say “You’re welcome”). (See examples below.)

## What is class P problem?

P-Class. The class P consists of those problems that are solvable in polynomial time, i.e. these problems can be solved in time O(nk) in worst-case, where k is constant. These problems are called tractable, while others are called intractable or superpolynomial.

## Are NP problems Decidable?

Remember P problems also fit the definition of NP, so…. There are certain NP-Hard problems that also exist in NP. They are decidable, verifiable in polynomial time and are a polynomial reduction of an NP problem.

## Can quantum computers solve NP-hard problems?

A quantum computer can solve any “search problem,” including many NP-hard problems, like SAT, in “checks”, where N is the size of the search space. This is with a general search algorithm called Grover’s algorithm . For example, for a SAT instance with n variables, there are possible ways to set all the variables.

## Is NP-hard in NP?

The complexity class of problems of this form is called NP, an abbreviation for “nondeterministic polynomial time”. A problem is said to be NP-hard if everything in NP can be transformed in polynomial time into it even though it may not be in NP. Conversely, a problem is NP-complete if it is both in NP and NP-hard.

## Are NP-hard problems solvable?

A problem is NP-hard if all problems in NP are polynomial time reducible to it, even though it may not be in NP itself. If a polynomial time algorithm exists for any of these problems, all problems in NP would be polynomial time solvable. These problems are called NP-complete.

## What kind of problems can a quantum computer solve?

Encryption and Cybersecurity These probably the most known kind of problems that quantum computers can solve. For example, the complex mathematical problem that is the core of the design of RSA encryption and other public-key encryption schemes is factoring a product of two prime numbers.

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