Can NP complete problems be solved in polynomial time?
The main thing to take away from an NP-complete problem is that it cannot be solved in polynomial time in any known way. NP-Hard/NP-Complete is a way of showing that certain classes of problems are not solvable in realistic time.
What operations is NP closed under?
3 Closure Properties for NP The class NP is closed under union, intersection, concatenation, and ∗.
Is NP closed under complementation?
NP is closed under union, intersection, and concatenation; but is not known to be closed under complement.
Are all problems in P solvable?
In computational complexity theory, P, also known as PTIME or DTIME(n), is a fundamental complexity class. It contains all decision problems that can be solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time.
Is NP-hard verifiable in polynomial time?
A NP problem (not NP-Hard problem) is a decision problem which can be verified in polynomial time. Maybe they are solvable in polynomial time, since all problems in P are also in NP . A NP-complete problem is a decision problem, which all NP problems can reduced to in polynomial time.
Which of the following Turing machines is capable of solving NP-complete problems in polynomial time?
It was recently proven mathematically that memcomputing machines have the same computational power of nondeterministic Turing machines. Therefore, they can solve NP-complete problems in polynomial time and, using the appropriate architecture, with resources that only grow polynomially with the input size.
Why is P closed under complement?
P is closed under complement. For any P-language L, let M be the TM that decides it in polynomial time. We construct a TM M’ that decides the complement of L in polynomial time: M’= “On input : 1.
Is L1 ∪ L2 necessarily in NP?
Then is L1 ∪ L2 ∈ NP? Ans: Yes, L1 ∪ L2 ∈ NP. We will prove it as follows.
Is P closed under star?
We show that P is closed under the star operation by dynamic programming. Let A be any language in P, and let M be the TM deciding A in polynomial time.
Does a Turing machine run in polynomial time?
A Turing machine M is polynomial time if ∀ inputs I of length n for sufficiently large n there exist c1,c2 such that M(I) halts in less than c1 · nc2 steps. A language L is in P if there exists a deterministic Turing machine M that decides L in polynomial time.
What is meant by non deterministic polynomial time?
Non-deterministic polynomial time (NP) is actually a marker used to point to a set of problems and bounds of the capability of certain types of computing. NP refers to the set of problems that can be solved in polynomial time by a non-deterministic Turing machine.
What is difference between NP-complete and NP-hard?
NP-Complete problems are as hard as NP problems….Difference between NP-Hard and NP-Complete:
| NP-hard | NP-Complete |
|---|---|
| To solve this problem, it do not have to be in NP . | To solve this problem, it must be both NP and NP-hard problems. |
| Do not have to be a Decision problem. | It is exclusively a Decision problem. |
Which of the following a Turing machine does not consist of?
3. Which of the following a turing machine does not consist of? Explanation: A state register is one which stores the state of the turing machine, one of the finitely many. Among these is the special start state with which the state register is initialized.
What is closed under complement?
A class is said to be closed under complement if the complement of any problem in the class is still in the class. Because there are Turing reductions from every problem to its complement, any class which is closed under Turing reductions is closed under complement.
Is Class P closed under intersection?
If x /∈ A then there is NO proof that x ∈ A. The class P is closed under union, intersection, concatenation, and ∗.
Are all P problems equivalent?
Therefore, the NP problem is now NP-complete, and NP = NP-complete. Both classes are equivalent.
What is a polynomial time Turing machine?
Definition 6 (P: Polynomial Time) A Turing machine M is polynomial time if ∀ inputs I of length n for sufficiently large n there exist c1,c2 such that M(I) halts in less than c1 · nc2 steps. A language L is in P if there exists a deterministic Turing machine M that decides L in polynomial time.
What is polynomial complexity?
An algorithm is said to have polynomial time complexity if its worst-case running time Tworst(n) T worst ( n ) for an input of size n is upper bounded by a polynomial p(n) for large enough n≥n0 n ≥ n 0 .
What is polynomial time problem?
A polynomial-time algorithm is an algorithm whose execution time is either given by a polynomial on the size of the input, or can be bounded by such a polynomial. Problems that can be solved by a polynomial-time algorithm are called tractable problems.
Why do we use nondeterministic polynomial time?
What Does Non-Deterministic Polynomial Time (NP) Mean? Non-deterministic polynomial time (NP) is actually a marker used to point to a set of problems and bounds of the capability of certain types of computing. NP refers to the set of problems that can be solved in polynomial time by a non-deterministic Turing machine.
What are the differences between both deterministic and nondeterministic?
Functions can be either deterministic or nondeterministic. A deterministic function always returns the same results if given the same input values. A nondeterministic function may return different results every time it is called, even when the same input values are provided.
Can NP-hard problems be verified in polynomial time?
An NP-Hard problem is one that is not solvable in polynomial time but can be verified in polynomial time.