Is P vs NP unsolvable?

Is P vs NP unsolvable?

Unsolved problem in computer science: If the solution to a problem is easy to check for correctness, must the problem be easy to solve? The P versus NP problem is a major unsolved problem in computer science.

Can a problem be P but not NP?

No NP-complete problems are known to be in P. If there is a polynomial-time algorithm for any NP-complete problem, then P = NP, because any problem in NP has a polynomial-time reduction to each NP-complete problem.

What does it mean if P is not equal to NP?

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.

Is it proven that P != NP?

The statement P=NP means that if a problem takes polynomial time on a non-deterministic TM, then one can build a deterministic TM which would solve the same problem also in polynomial time. So far nobody has been able to show that it can be done, but nobody has been able to prove that it cannot be done, either.

Is Sudoku An NP?

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 chess a NP?

For this reason games like chess cannot themselves be NP-complete, as they only have a finite (albeit unthinkably large) number of possible positions.

What is the difference between P and NP?

P = the set of problems that are solvable in polynomial time by a Deterministic Turing Machine. NP = the set of decision problems (answer is either yes or no) that are solvable in nondeterministic polynomial time i.e can be solved in polynomial time by a Nondeterministic Turing Machine[4].

How hard is P vs NP?

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.

Are all NP problems NP-complete?

A problem is called NP (nondeterministic polynomial) if its solution can be guessed and verified in polynomial time; nondeterministic means that no particular rule is followed to make the guess. If a problem is NP and all other NP problems are polynomial-time reducible to it, the problem is NP-complete.

Is Minesweeper NP hard?

Minesweeper Consistency is NP Complete Since Minesweeper Consistency has been shown to be in NP and is NP Hard, by definition, it is NP Complete.


1 Answer. Show activity on this post. Any problem in NP is in EXPTIME because you can either use exponential time to try all possible certificates or to enumerate all possible computation paths of a nondeterministic machine.

What is the P vs NP problem?

The P versus NP problem is a major unsolved problem in computer science. It asks whether every problem whose solution can be quickly verified (technically, verified in polynomial time) can also be solved quickly (again, in polynomial time).

What are the types of computations that do not follow P and NP?

Finally, there are types of computations which do not conform to the Turing machine model on which P and NP are defined, such as quantum computation and randomized algorithms . Cook provides a restatement of the problem in THE P VERSUS NP PROBLEM as: Does P = NP?.

What is the difference between NP-complete and NP-hard problems?

Informally, an NP -complete problem is an NP problem that is at least as “tough” as any other problem in NP. NP -hard problems are those at least as hard as NP problems; i.e., all NP problems can be reduced (in polynomial time) to them. NP -hard problems need not be in NP; i.e., they need not have solutions verifiable in polynomial time.

Is Boolean satisfiability a NP-complete problem?

The Boolean satisfiability problem is one of many such NP -complete problems. If any NP -complete problem is in P, then it would follow that P = NP. However, many important problems have been shown to be NP -complete, and no fast algorithm for any of them is known.