What languages are NP-complete?
L. A language in L is called NP-complete iff L is NP-hard and L ∈ NP. The class NPC is the set of NP-complete problems. Theorem: If any NP-complete language is in P, then P = NP.
What is the difference between Class P and Class NP?
Step 1 − If a problem is in class P, it is nothing but we can find a solution to that type of problem in polynomial time. Step 2 − If a problem is in class NP, it is nothing but that we can verify a possible solution in polynomial time.
Is NP and NP-complete the same?
“Complete” refers to the property of being able to simulate everything in the same complexity class. Conversely, a problem is NP-complete if it is both in NP and NP-hard. The NP-complete problems represent the hardest problems in NP. If some NP-complete problem has a polynomial time algorithm, all problems in NP do.
Is NP-complete the hardest?
Problems that are NP-hard do not have to be elements of NP; indeed, they may not even be decidable. NP-complete. Class of decision problems which contains the hardest problems in NP. Each NP-complete problem has to be in NP.
Can a language in P be NP-complete?
P is the set of all polynomial-time computable languages. The definition of nondeterministic polynomial-time computable is almost the same, except that the turing machine is allowed to be nondeterministic. A language is NP-complete if it is both NP-hard and NP.
Is P NP-complete?
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.
What is P and NP class problems?
P is set of problems that can be solved by a deterministic Turing machine in Polynomial time. • NP is set of problems that can be solved by a Non-deterministic Turing Machine in Polynomial time.
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).
What is the hardest NP problem?
NP-complete problems are the hardest problems in the NP set. A decision problem L is NP-complete if: 1) L is in NP (Any given solution for NP-complete problems can be verified quickly, but there is no efficient known solution). 2) Every problem in NP is reducible to L in polynomial time (Reduction is defined below).
What languages are not in NP?
All languages in P and NP are decidable. Any undecidable language, such as the halting problem, cannot be in NP. The nondeterministic time hierarchy theorem can be used to show that there are languages in NEXP that are not in NP.
What is the difference between problems in P and NP-complete?
All problems in P can be solved with polynomial time algorithms, whereas all problems in NP – P are intractable. 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 is NP class in Computer Science?
NP-Class The class NP consists of those problems that are verifiable in polynomial time. NP is the class of decision problems for which it is easy to check the correctness of a claimed answer, with the aid of a little extra information.
Is it possible to prove P = 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. The problem belongs to class P if it’s easy to find a solution for the problem.
Do NP class problems have a polynomial run time?
In essence, NP class problems don’t have a polynomial run-time to solve, but have a polynomial run-time to verify solutions (difficult to solve, easy to check a given answer). I can’t really explain this one outside of using examples, so: we have two problems, A and B, and we know problem B is a P class problem.