What is an example of an NP-complete problem?
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.
Can a problem be NP-complete and co-NP?
Each co-NP-complete problem is the complement of an NP-complete problem. There are some problems in both NP and co-NP, for example all problems in P or integer factorization. However, it is not known if the sets are equal, although inequality is thought more likely. See co-NP and NP-complete for more details.
How do you prove a problem is co-NP-complete?
We show that ˉL is coNP-complete, that is, for every language A∈coNP, A≤ˉL. Let A∈coNP. Then ˉA is in NP. By NP-completeness of L, there exists a function f, computable in polynomial time such that x∈ˉA iff f(x)∈L.
How many NP problems are there?
We provide Ising formulations for many NP-complete and NP-hard problems, including all of Karp’s 21 NP-complete problems. This collects and extends mappings to the Ising model from partitioning, covering, and satisfiability.
Is Sudoku NP-complete?
Sudoku is NP-complete when generalized to a n × n grid however a standard 9 × 9 Sudoku is not NP- complete.
What is NP-hard problems explain with examples?
Another example of an NP-hard problem is the optimization problem of finding the least-cost cyclic route through all nodes of a weighted graph. This is commonly known as the travelling salesman problem. There are decision problems that are NP-hard but not NP-complete such as the halting problem.
What are co-NP problems?
That is, co-NP is the set of decision problems where there exists a polynomial p(n) and a polynomial-time bounded Turing machine M such that for every instance x, x is a no-instance if and only if: for some possible certificate c of length bounded by p(n), the Turing machine M accepts the pair (x, c).
Is every decision problem in NP or co-NP?
CoNP is the class of decision problems for which there is a polynomial time algorithm that can verify “no” instances given the appropriate certificate. We don’t know whether coNP is different from NP. There is a problem in NP for every problem in coNP, and vice versa.
What is you understanding on NP and co-NP problems?
NP is the class of decision problems for which there is a polynomial time algorithm that can verify “yes” instances given the appropriate certificate. CoNP is the class of decision problems for which there is a polynomial time algorithm that can verify “no” instances given the appropriate certificate.
Is Unsat NP-hard?
If SAT-UNSAT ∈NP, then SAT-UNSAT is NP-complete. This implies things such that the problem UNSAT (which is coNP-complete) is NP-hard since we can reduce UNSAT to SAT-UNSAT which is NP-complete.
Is Battleship NP-complete?
This reduction proves that BATTLESHIPS is NP-hard. It is easy to see that a non-deterministic guess is checked to be a solution in polynomial time. Hence BATTLESHIPS is NP-complete.
How many possible Sudokus are there?
6,670,903,752,021,072,936,960 possible
There are 6,670,903,752,021,072,936,960 possible solvable Sudoku grids that yield a unique result (that’s 6 sextillion, 670 quintillion, 903 quadrillion, 752 trillion, 21 billion, 72 million, 936 thousand, 960 in case you were wondering). That’s way more than the number of stars in the universe.
Is Sudoku always solvable?
Harder Still… So, armed with all of these potential techniques, you’ll be able to solve all possible Sudoku? Well, maybe, maybe not. The vast majority of puzzles don’t require the trickier techniques, but there are some which just aren’t solvable by simple logic alone, and require various forms of guessing to solve.
What are tractable problems?
Tractable problem, in computational complexity theory, a problem that can be solved in polynomial time. Tractable, ease of obtaining a mathematical solution such as a closed-form expression.
Is co-NP contained in NP?
From this, it follows that the set of complements of the problems in NP is a subset of the set of complements of the problems in co-NP; i.e., co-NP ⊆ NP. Thus co-NP = NP. The proof that no co-NP-complete problem can be in NP if NP ≠ co-NP is symmetrical.
Why are NP and CoNP different?
Is SAT an NPC?
SAT is NP-complete: the Cook-Levin Theorem Given a boolean expression E of length n, a multitape nondeterministic Turing machine can guess a truth assignment T for E in O(n) time. The NTM can then evaluate E using the truth assignment T in O(n2) time.
Is Boolean satisfiability NP-complete?
SAT is the first problem that was proven to be NP-complete; see Cook–Levin theorem. This means that all problems in the complexity class NP, which includes a wide range of natural decision and optimization problems, are at most as difficult to solve as SAT.