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- Schaefers_dichotomy_theorem abstract "In computational complexity theory, a branch of computer science, Schaefer's dichotomy theorem states necessary and sufficient conditions under which a finite set S of relations over the Boolean domain yields polynomial-time or NP-complete problems when the relations of S are used to constrain some of the propositional variables.It is called a dichotomy theorem because the complexity of the problem defined by S is either in P or NP-complete as opposed to one of the classes of intermediate complexity that is known to exist (assuming P ≠ NP) by Ladner's theorem.Special cases of Schaefer's dichotomy theorem include the NP-completeness of SAT (the Boolean satisfiability problem) and its two popular variants 1-in-3 SAT and Not-All-Equal 3SAT (often denoted by NAE-3SAT). In fact, for these two variants of SAT, Schaefer's dichotomy theorem shows that their monotone versions (where negations of variables are not allowed) are also NP-complete.".
- Schaefers_dichotomy_theorem wikiPageID "4638322".
- Schaefers_dichotomy_theorem wikiPageLength "10407".
- Schaefers_dichotomy_theorem wikiPageOutDegree "24".
- Schaefers_dichotomy_theorem wikiPageRevisionID "679402390".
- Schaefers_dichotomy_theorem wikiPageWikiLink Boolean_domain.
- Schaefers_dichotomy_theorem wikiPageWikiLink Boolean_satisfiability_problem.
- Schaefers_dichotomy_theorem wikiPageWikiLink Category:Constraint_programming.
- Schaefers_dichotomy_theorem wikiPageWikiLink Category:Theorems_in_computational_complexity_theory.
- Schaefers_dichotomy_theorem wikiPageWikiLink Computational_complexity_theory.
- Schaefers_dichotomy_theorem wikiPageWikiLink Computer_science.
- Schaefers_dichotomy_theorem wikiPageWikiLink Constraint_satisfaction_problem.
- Schaefers_dichotomy_theorem wikiPageWikiLink Decision_problem.
- Schaefers_dichotomy_theorem wikiPageWikiLink Galois_connection.
- Schaefers_dichotomy_theorem wikiPageWikiLink Horn_clause.
- Schaefers_dichotomy_theorem wikiPageWikiLink L_(complexity).
- Schaefers_dichotomy_theorem wikiPageWikiLink Ladners_theorem.
- Schaefers_dichotomy_theorem wikiPageWikiLink Ones_classification_theorems.
- Schaefers_dichotomy_theorem wikiPageWikiLink NL-complete.
- Schaefers_dichotomy_theorem wikiPageWikiLink NP-complete.
- Schaefers_dichotomy_theorem wikiPageWikiLink NP-completeness.
- Schaefers_dichotomy_theorem wikiPageWikiLink NP-intermediate.
- Schaefers_dichotomy_theorem wikiPageWikiLink One-in-three_3SAT.
- Schaefers_dichotomy_theorem wikiPageWikiLink P-complete.
- Schaefers_dichotomy_theorem wikiPageWikiLink P_(complexity).
- Schaefers_dichotomy_theorem wikiPageWikiLink P_versus_NP_problem.
- Schaefers_dichotomy_theorem wikiPageWikiLink Propositional_variable.
- Schaefers_dichotomy_theorem wikiPageWikiLink Reduction_(complexity).
- Schaefers_dichotomy_theorem wikiPageWikiLink Sharp-P-complete.
- Schaefers_dichotomy_theorem wikiPageWikiLink Universal_algebra.
- Schaefers_dichotomy_theorem wikiPageWikiLinkText "Schaefer's dichotomy theorem".
- Schaefers_dichotomy_theorem hasPhotoCollection Schaefers_dichotomy_theorem.
- Schaefers_dichotomy_theorem wikiPageUsesTemplate Template:Reflist.
- Schaefers_dichotomy_theorem subject Category:Constraint_programming.
- Schaefers_dichotomy_theorem subject Category:Theorems_in_computational_complexity_theory.
- Schaefers_dichotomy_theorem comment "In computational complexity theory, a branch of computer science, Schaefer's dichotomy theorem states necessary and sufficient conditions under which a finite set S of relations over the Boolean domain yields polynomial-time or NP-complete problems when the relations of S are used to constrain some of the propositional variables.It is called a dichotomy theorem because the complexity of the problem defined by S is either in P or NP-complete as opposed to one of the classes of intermediate complexity that is known to exist (assuming P ≠ NP) by Ladner's theorem.Special cases of Schaefer's dichotomy theorem include the NP-completeness of SAT (the Boolean satisfiability problem) and its two popular variants 1-in-3 SAT and Not-All-Equal 3SAT (often denoted by NAE-3SAT). ".
- Schaefers_dichotomy_theorem label "Schaefer's dichotomy theorem".
- Schaefers_dichotomy_theorem sameAs m.0cdxv1.
- Schaefers_dichotomy_theorem sameAs Q7430892.
- Schaefers_dichotomy_theorem sameAs Q7430892.
- Schaefers_dichotomy_theorem wasDerivedFrom Schaefers_dichotomy_theoremoldid=679402390.
- Schaefers_dichotomy_theorem isPrimaryTopicOf Schaefers_dichotomy_theorem.