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A decision problem is a computational problem where the answer for every instance is either yes or no. An example of a decision problem is primality testing: "Given a positive integer n, determine if n is prime." A decision problem is typically represented as the set of all instances for which the answer is yes. For example, primality testing ...
NP is a class of decision problems; the analogous class of function problems is FNP. The only known strict inclusions come from the time hierarchy theorem and the space hierarchy theorem , and respectively they are N P ⊊ N E X P T I M E {\displaystyle {\mathsf {NP\subsetneq NEXPTIME}}} and N P ⊊ E X P S P A C E {\displaystyle {\mathsf {NP ...
"A large-scale quantum computer would be able to efficiently solve NP-complete problems." The class of decision problems that can be efficiently solved (in principle) by a fault-tolerant quantum computer is known as BQP. However, BQP is not believed to contain all of NP, and if it does not, then it cannot contain any NP-complete problem. [15]
The program is solvable in polynomial time if the graph has all undirected or all directed edges. Variants include the rural postman problem. [3]: ND25, ND27 Clique cover problem [2] [3]: GT17 Clique problem [2] [3]: GT19 Complete coloring, a.k.a. achromatic number [3]: GT5 Cycle rank; Degree-constrained spanning tree [3]: ND1
A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.
If there is an algorithm (say a Turing machine, or a computer program with unbounded memory) that produces the correct answer for any input string of length n in at most cn k steps, where k and c are constants independent of the input string, then we say that the problem can be solved in polynomial time and we place it in the class P. Formally ...
A variant of the 3-satisfiability problem is the one-in-three 3-SAT (also known variously as 1-in-3-SAT and exactly-1 3-SAT). Given a conjunctive normal form with three literals per clause, the problem is to determine whether there exists a truth assignment to the variables so that each clause has exactly one TRUE literal (and thus exactly two ...
A clique problem for a class of so-called M-graphs. It is shown that finding an isomorphism for n-vertex graphs is equivalent to finding an n-clique in an M-graph of size n 2. This fact is interesting because the problem of finding a clique of order (1 − ε)n in a M-graph of size n 2 is NP-complete for arbitrarily small positive ε. [43]