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What is the class of the NP complete problems?
NP-complete problem, any of a class of computational problems for which no efficient solution algorithm has been found. Many significant computer-science problems belong to this class—e.g., the traveling salesman problem, satisfiability problems, and graph-covering problems.
What is a class NP decision problem?
NP is the set of decision problems for which the problem instances, where the answer is “yes”, have proofs verifiable in polynomial time by a deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine.
How do we show a problem belongs to the class NP?
The easiest way to prove some problem is in NP is using the certificate definiiton of NP mentioned in other answers. The nondeterministic definition of NP is usually not very useful for showing a problem belongs to NP.
What does NP class mean?
Nondeterministic Polynomial Time
From last class we have a formal definition of the class NP. “NP” stands for “Nondeterministic Polynomial Time”, meaning the class of problems that can be solved in polynomial time on a nondeterministic machine.
Are P problems in NP?
P is the set of problems whose solution times are proportional to polynomials involving N’s. NP (which stands for nondeterministic polynomial time) is the set of problems whose solutions can be verified in polynomial time. But as far as anyone can tell, many of those problems take exponential time to solve.
Is halting a problem with NP?
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.
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.
When is a problem in a class NP hard?
A problem is in the class NPC if it is in NP and is as hard as any problem in NP. 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.
Which is the best definition of the complexity class NP?
In computational complexity theory, NP ( nondeterministic polynomial time) is a complexity class used to classify decision problems. NP is the set of decision problems for which the problem instances, where the answer is “yes”, have proofs verifiable in polynomial time by a non deterministic Turing machine.
Is it possible to prove that P is NP?
It is not known whether P = NP. However, many problems are known in NP with the property that if they belong to P, then it can be proved that P = NP. If P ≠ NP, there are problems in NP that are neither in P nor in NP-Complete.
What are the advantages of the class NP?
The advantages in considering the class of polynomial-time algorithms is that all reasonable deterministic single processor model of computation can be simulated on each other with at most a polynomial slow-d The class NP consists of those problems that are verifiable in polynomial time.