Is there a problem in NP that has a polynomial time algorithm?

Strictly speaking, as the other answers explain, no. A polynomial-time algorithm for an NP-hard problem is not known nor expected to exist.

Are NP-hard problems verifiable in polynomial time?

An NP-Hard problem is one that is not solvable in polynomial time but can be verified in polynomial time.

Is set of problems that can be solved in polynomial time?

Problems that can be solved in polynomial time are called Tractable problems.

Will P vs NP ever 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 happens if P vs NP is 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 NP-hard reduce to NP-complete?

Can all NP-hard problems be reduced to one another?: No. And NP-hard means, all problems in NP can be reduced to one NP-hard one, but not the other way around, since not all NP-hard problems are also in NP.

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. … The NP-complete problems represent the hardest problems in NP.

Is NP a Pspace?

Since, PSPACE is closed under reductions and NP is contained in PSPACE, then we have that NP = PSPACE. The P versus NP problem is a major unsolved problem in computer science. This problem was introduced in 1971 by Stephen Cook [1]. It is considered by many to be the most important open problem in the field [2].

Is Sudoku NP-complete?

Introduction. The generalised Sudoku problem is an NP-complete problem which, effectively, requests a Latin square that satisfies some additional constraints. In addition to the standard requirement that each row and column of the Latin square contains each symbol precisely once, Sudoku also demands block constraints.

Is TSP NP-complete?

Traveling Salesman Optimization(TSP-OPT) is a NP-hard problem and Traveling Salesman Search(TSP) is NP-complete. However, TSP-OPT can be reduced to TSP since if TSP can be solved in polynomial time, then so can TSP-OPT(1).

Is halt NP-complete?

– If we had a polynomial time algorithm for the halting problem, then we could solve the satisfiability problem in polynomial time using A and X as input to the algorithm for the halting problem . – Hence the halting problem is an NP-hard problem which is not in NP. – So it is not NP-complete.

Is NP equal to P?

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.

Is Sudoku polynomial time?

First of all, solving 4×4 Sudoku is a Polynomial-time problem.

Is 9×9 Sudoku NP-complete?

Sudoku is NP-complete when generalized to a n × n grid however a standard 9 × 9 Sudoku is not NP- complete.

What does NP mean Cs?

Non-deterministic 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). Basically, a solution has to be testable in poly time.

Why P NP is important?

Now, if P=NP, we could find solutions to search problems as easily as checking whether those solutions are good. This would essentially solve all the algorithmic challenges that we face today and computers could solve almost any task.

Is PA a subset of NP?

P is subset of NP (any problem that can be solved by a deterministic machine in polynomial time can also be solved by a non-deterministic machine in polynomial time).

Is prime factorization NP-complete?

The prime factorization problem is in the NP class, but we don’t know if it is NP-hard. In other words, there is currently no proof that prime factorization problem cannot be solved polynomial time (= in P).

Can you reduce P to NP?

Quick reply: No, it does not. Recall the definition of NP-hard problems. A problem X is NP-Hard if every problem in NP can be polynomially reduced to X. If on the other hand a problem X can be polynomially reduced to some NP-complete problem Y, it means that Y is at least as hard as X, not the other way around.

Is NP No problem?

NP stands for “No problem.” It’s usually used as a replacement for “You’re welcome” when thanks is offered.

Is factorization NP-hard?

Integer factorization is not NP-hard (so not NP-complete). … So, while doing a polynomial-time integer factorization would be hugely significant (and make all asymmetric encryption in the world useless), it would not prove P=NP.