Is This Proof of Existence and a Solution to P=NP Problem?

Is there a proof for P NP?

1: It is impossible to prove that P =NP in the deterministic or time inde- pendent framework of Mathematics.

Is P versus NP problem 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.

How do you prove a problem is NP problem?

To prove that problem A is NP-hard, reduce a known NP-hard problem to A. In other words, to prove that your problem is hard, you need to describe an ecient algorithm to solve a dierent problem, which you already know is hard, using an hypothetical ecient algorithm for your problem as a black-box subroutine.

Is P NP solvable?

P is the set of all decision problems that are efficiently solvable. P is a subset of NP. P is the set of all decision problems that are efficiently solvable and is a subset of NP. Basic Arithmetic is solvable in Polynomial-time, thus belongs to P.

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).

What was the first problem proved to be NP-complete?

SAT (Boolean satisfiability problem) is the first NP-Complete problem proved by Cook (See CLRS book for proof). It is always useful to know about NP-Completeness even for engineers.

How do you solve NP-complete problems?


  1. Use a heuristic. If you can’t quickly solve the problem with a good worst case time, maybe you can come up with a method for solving a reasonable fraction of the common cases.
  2. Solve the problem approximately instead of exactly. …
  3. Use an exponential time solution anyway. …
  4. Choose a better abstraction.

How many steps are required to prove that a decision problem is NP-complete *?

How many steps are required to prove that a decision problem is NP complete? Explanation: First, the problem should be NP. Next, it should be proved that every problem in NP is reducible to the problem in question in polynomial time.

Can NP-hard problems be solved?

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.

Are NP-hard problems solvable?

No, if a problem is NP-complete then it is not solvable in polynomial time unless P=NP, which has not been proven yet. Furthermore, if there were any NP-hard problem which would be solvable in polynomial time then (by reduction) it could be used to solve any other problem in NP, thus implying P=NP.

Can quantum computers solve NP problems?

Contrary to myth, quantum computers are not known to be able to solve efficiently the very hard class called NP-complete problems.

Will quantum computers solve everything?

The current —and rather harsh—truth is that there aren’t really any real-world problems only solvable with a quantum computer. At least not right now. Anything we currently care about can most likely be solved on a classical computer if you give it a few million or billion years (and plenty of power).

What problems has quantum computing solved?

A quantum computer just solved a decades-old problem three million times faster than a classical computer. Using a method called quantum annealing, D-Wave’s researchers demonstrated that a quantum computational advantage could be achieved over classical means.

Is Google a quantum computer?

In 2019, Google announced that its Sycamore quantum computer had completed a task in 200 seconds that would take a conventional computer 10,000 years.

Is Quantum AI possible?

Quantum computing can be used for the rapid training of machine learning models and to create optimized algorithms. An optimized and stable AI provided by quantum computing can complete years of analysis in a short time and lead to advances in technology.

Who invented quantum computing?

Quantum computers were proposed in the 1980s by Richard Feynman and Yuri Manin. The intuition behind quantum computing stemmed from what was often seen as one of the greatest embarrassments of physics: remarkable scientific progress faced with an inability to model even simple systems.

How big is a time crystal?

We find that time crystals can be created with sizes in the range s ≈ 20–100 and that such big time crystals are easier to realize experimentally than a period-doubling (s=2) time crystal because they require either a larger drop height or a smaller number of bounces on the mirror.

How big is Google’s quantum computer?

An example: A simple quantum computer is about the size of a room, featuring a cryostat that maintains the quantum processor at a super-cold temperature of about 10 milliKelvin – making the cryostat one of the coldest places in the known universe.

How fast is a quantum computer?

Quantum computing is a new generation of technology that involves a type of computer 158 million times faster than the most sophisticated supercomputer we have in the world today. It is a device so powerful that it could do in four minutes what it would take a traditional supercomputer 10,000 years to accomplish.

What are Google’s time crystals?

A team of researchers including ones from Stanford and Google have created and observed a new phase of matter, popularly known as a time crystal. There is a huge global effort to engineer a computer capable of harnessing the power of quantum physics to carry out computations of unprecedented complexity.

Can we reverse time?

Yes, you really can turn back time—with a catch. A new paper suggests that time can actually flow forward and backward. Microscopic systems can naturally evolve toward lower entropy, meaning they could return to a prior state. Humans don’t perceive these micro phenomenons at the quantum level.

What are quantum crystals?

A quantum crystal is one in which the zero point motion of an atom about its equilibrium position is a large fraction of the near neighbor distance. Both short range correlations and long range correlations (phonons) are of importance and must be treated with care in the description of quantum crystals.