## Are NP-hard problems NP complete?

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.

Is Bitcoin NP-hard?

As it turns out, this requires solving two optimization problems, both of which are NP-hard! …

Has anyone solved NP or P?

Now, a German man named Norbert Blum has claimed to have solved the above riddle, which is properly known as the P vs NP problem. Unfortunately, his purported solution doesn’t bear good news. Blum, who is from the University of Bonn, claims in his recently published 38-page paper that P does not equal NP.

### Is NP harder than P?

The P versus NP problem is a major unsolved problem in computer science. If it turned out that P ≠ NP, which is widely believed, it would mean that there are problems in NP that are harder to compute than to verify: they could not be solved in polynomial time, but the answer could be verified in polynomial time.

Is traveling salesman NP-hard?

The travelling salesman problem (also called the traveling salesperson problem or TSP) asks the following question: “Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?” It is an NP-hard problem in …

Can P be reduced 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.

#### What happens if P NP?

If P=NP, then all of the NP problems can be solved deterministically in Polynomial time. This is because the NP problems are all essentially the same problem, just stated in different terms.

What is meant by NP hard?

A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP- problem (nondeterministic polynomial time) problem. NP-hard therefore means “at least as hard as any NP-problem,” although it might, in fact, be harder.

Is P NP If no then what will happen if P will become equal to NP?

## What is harder than NP-hard?

There are complexity classes more “difficult” than NP, for example PSPACE, EXPTIME or EXPSPACE, and all these contain NP-hard but not NP-complete problems. Turing halting problem is undecidable and it belongs to NP-Hard set.

Why is NP-hard not in NP?

An NP-hard problem can be beyond NP. The polynomial-time reduction from your X to any problem in NP does not necessarily have a polynomial-time inverse. If the inverse is harder, then the verification is harder.

What’s the difference between NP hard and NP complete problems?

The NP problems set of problems whose solutions are hard to find but easy to verify and are solved by Non-Deterministic Machine in polynomial time. A Problem X is NP-Hard if there is an NP-Complete problem Y, such that Y is reducible to X in polynomial time. NP-Hard problems are as hard as NP-Complete problems.

### Are there any polynomial time algorithms for NP hard problems?

NP, it is unlikely that such an algorithm exists. A common misconception is that the NP in “NP-hard” stands for “non-polynomial” when in fact it stands for ” non-deterministic polynomial acceptable problems”. It is suspected that there are no polynomial-time algorithms for NP-hard problems, but that has not been proven.

Is the halting problem in NP a decidable problem?

It is also easy to see that the halting problem is not in NP since all problems in NP are decidable in a finite number of operations, but the halting problem, in general, is undecidable. There are also NP-hard problems that are neither NP-complete nor Undecidable.

When was the P versus NP problem introduced?

The precise statement of the P versus NP problem was introduced in 1971 by Stephen Cook in his seminal paper “The complexity of theorem proving procedures”. In order to correctly understand the P versus NP problem, basic knowledge of computational complexity is a must.

Are NP-hard problems NP complete? 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…