Unsolved problem in computer science: ⁠ NP   = ?   co-NP {\displaystyle {\textsf {NP}}\ {\overset {?}{=}}\ {\textsf {co-NP}}} ⁠ (more unsolved problems in computer...

computational problems that are co-NP-complete are those that are the hardest problems in co-NP, in the sense that any problem in co-NP can be reformulated as...

since P = NP if and only if P = PH (as the former would establish that NP = co-NP, which in turn implies that NP = PH). No known algorithm for a NP-complete...

be in NP. 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...

Look up np in Wiktionary, the free dictionary. NP may refer to: NP (novel), by Japanese author Banana Yoshimoto Nashua-Plainfield Community School District...

{\mathsf {P\ {\overset {?}{=}}\ NP}}} (more unsolved problems in computer science) In computational complexity theory, NP (nondeterministic polynomial time)...

hierarchy) is a hierarchy of complexity classes that generalize the classes NP and co-NP. Each class in the hierarchy is contained within PSPACE. The hierarchy...

which this is true for the "no" instances is called co-NP. P is trivially a subset of NP and of co-NP; most experts believe it is a proper subset, although...

language L is in NP then the complement of L is in co-NP. (This does not mean that the complement of NP is co-NP—there are languages which are known to be in...

seven qubits. In order to talk about complexity classes such as P, NP, and co-NP, the problem has to be stated as a decision problem. Decision problem (Integer...

contained in NP and co-NP. There is even an oracle in which ⁠ B P P = E X P N P {\displaystyle {\mathsf {BPP}}={\mathsf {EXP}}^{\mathsf {NP}}} ⁠ (and hence...

evidence that these problems are not NP-complete, since if they were, it would imply that NP is subset of co-NP, a result widely believed to be false;...

In computational complexity theory, NP/poly is a complexity class, a non-uniform analogue of the class NP of problems solvable in polynomial time by a...

{\mathsf {NP}}\cap {\mathsf {coNP}}={\mathsf {P}}} then F ( N P ∩ c o N P ) = F P {\displaystyle {\mathsf {F}}({\mathsf {NP}}\cap {\mathsf {coNP}})={\mathsf...

guaranteed to be consistent, solving it is not known to be NP-complete, but it has been proven to be co-NP-complete. In the latter case, however, minesweeper...

co-RP, or whether RP is a subset of the intersection of NP and co-NP, though this would be implied by P = BPP. A natural example of a problem in co-RP...

quadratic nonresidue problem has both an NP and a co-NP algorithm, and so lies in the intersection of NP and co-NP. This was also true of several other problems...

propositional proof systems can be viewed as a step towards separating NP from coNP (and thus P from NP), since the existence of a propositional proof system that...

problems that are in the complexity class NP but are neither in the class P nor NP-complete are called NP-intermediate, and the class of such problems...

whereas classes that lack a recursive enumeration have none. For example, NP, co-NP, PLS, PPA all have known natural complete problems. There are classes...

properties: the satisfiability problem continues to be NP-complete, and the validity problem continues to be co-NP-complete. For formulas in conjunctive normal...

PSPACE, meaning that co-PSPACE = PSPACE. The following relations are known between PSPACE and the complexity classes NL, P, NP, PH, EXPTIME and EXPSPACE...

that the complement of the graph isomorphism problem, a co-NP problem not known to be in NP, has an AM algorithm and the best way to see it is via a...

about proposed solutions. P versus NP problem What is the relationship between BQP and NP? NC = P problem NP = co-NP problem P = BPP problem P = PSPACE...

generalizes the rules used in the definition of the complexity classes NP and co-NP. The concept of an ATM was set forth by Chandra and Stockmeyer and independently...

language in co-NP that does not have an interactive protocol. In November 1989, Fortnow received an email from Noam Nisan showing that co-NP had multiple...

{\displaystyle NP\cap coNP} are also called well-characterized problems. It is a long-standing open question whether N P ∩ c o N P {\displaystyle NP\cap coNP} is...

{X}}\}} ). co-NP, for instance, is one important complement complexity class, and sits at the center of the unsolved problem over whether co-NP=NP. Closure...

contains any FNP-complete problem it follows that N P = co-NP {\displaystyle \mathbf {NP} ={\textbf {co-NP}}} . Decision problem Search problem Counting problem...

Charles H.; Gill, John (1981), "Relative to a Random Oracle A, P^A != NP^A != co-NP^A with Probability 1", SIAM Journal on Computing, 10 (1): 96–113, doi:10...