Max-3-SAT
E537214
Max-3-SAT is an optimization variant of the Boolean satisfiability problem where the goal is to maximize the number of satisfied clauses, each containing exactly three literals, and it serves as a central problem in the study of approximation algorithms and hardness of approximation.
All labels observed (2)
How this entity was disambiguated
This entity first appeared as the object of triple T5642217 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Max-3-SAT Context triple: [Inapproximability results for SAT and other problems, relatedConcept, Max-3-SAT]
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A.
“Inapproximability results for SAT and other problems”
“Inapproximability results for SAT and other problems” is a seminal theoretical computer science paper by Johan Håstad that establishes tight hardness-of-approximation bounds for satisfiability and related optimization problems using probabilistically checkable proofs.
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B.
TNTSAT
TNTSAT is a French free-to-air satellite television platform that broadcasts the national digital terrestrial TV channels via satellite.
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C.
Cook–Levin theorem
The Cook–Levin theorem is a foundational result in computational complexity theory that established the Boolean satisfiability problem (SAT) as the first NP-complete problem, launching the theory of NP-completeness.
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D.
NP-completeness
NP-completeness is a central concept in computational complexity theory that classifies decision problems believed to be among the hardest in NP, such that a polynomial-time solution to any one of them would yield polynomial-time solutions to all problems in NP.
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E.
P versus NP problem
The P versus NP problem is a central unsolved question in theoretical computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Max-3-SAT Target entity description: Max-3-SAT is an optimization variant of the Boolean satisfiability problem where the goal is to maximize the number of satisfied clauses, each containing exactly three literals, and it serves as a central problem in the study of approximation algorithms and hardness of approximation.
-
A.
“Inapproximability results for SAT and other problems”
“Inapproximability results for SAT and other problems” is a seminal theoretical computer science paper by Johan Håstad that establishes tight hardness-of-approximation bounds for satisfiability and related optimization problems using probabilistically checkable proofs.
-
B.
TNTSAT
TNTSAT is a French free-to-air satellite television platform that broadcasts the national digital terrestrial TV channels via satellite.
-
C.
Cook–Levin theorem
The Cook–Levin theorem is a foundational result in computational complexity theory that established the Boolean satisfiability problem (SAT) as the first NP-complete problem, launching the theory of NP-completeness.
-
D.
NP-completeness
NP-completeness is a central concept in computational complexity theory that classifies decision problems believed to be among the hardest in NP, such that a polynomial-time solution to any one of them would yield polynomial-time solutions to all problems in NP.
-
E.
P versus NP problem
The P versus NP problem is a central unsolved question in theoretical computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
computational problem
ⓘ
constraint satisfaction problem ⓘ |
| basedOn | 3-SAT ⓘ |
| clauseType | disjunction of three literals ⓘ |
| complexityClass | NP-hard ⓘ |
| decisionVersion | is there an assignment satisfying at least k clauses? ⓘ |
| expectedSatisfiedFractionUnderRandomAssignment | 7/8 ⓘ |
| formulaStructure | conjunction of 3-literal clauses ⓘ |
| generalizationOf | 3-SAT ⓘ |
| hasAlternativeObjectiveFunction | fraction of satisfied clauses ⓘ |
| hasApproximationAlgorithm | randomized 7/8-approximation ⓘ |
| hasApproximationGuarantee | no polynomial-time algorithm can beat 7/8 + ε under P≠NP (for some formulations) ⓘ |
| hasApproximationRatio | 7/8 by random assignment ⓘ |
| hasConstraint | each clause has exactly three literals ⓘ |
| hasInput | 3-CNF formula ⓘ |
| hasObjective | maximize number of satisfied clauses ⓘ |
| hasRandomizedBaseline | assign each variable true or false independently with probability 1/2 ⓘ |
| hasReductionFrom | 3-SAT ⓘ |
| hasReductionTo |
Max-Cut (via standard transformations in hardness proofs)
ⓘ
Max-SAT ⓘ |
| hasTypicalObjectiveFunction | number of satisfied clauses ⓘ |
| hasVariableDomain | Boolean variables ⓘ |
| isCentralIn |
design of randomized approximation algorithms
ⓘ
study of inapproximability ⓘ |
| isRobustVariantOf | 3-SAT with respect to unsatisfiable instances ⓘ |
| isSpecialCaseOf |
Max-CSP
ⓘ
Max-k-SAT ⓘ
linked to:
Max-SAT
|
| literalType | variable or its negation ⓘ |
| optimizationCriterion | maximize satisfied clauses rather than satisfy all ⓘ |
| output |
maximum number of satisfiable clauses
ⓘ
truth assignment ⓘ |
| relatedTo |
3-SAT
ⓘ
Boolean satisfiability problem ⓘ Max-SAT ⓘ approximation algorithms ⓘ hardness of approximation ⓘ |
| searchSpace | all truth assignments to Boolean variables ⓘ |
| studiedIn |
approximation complexity
ⓘ
probabilistically checkable proofs ⓘ theory of NP-completeness ⓘ |
| usedAs |
benchmark problem in approximation algorithms
ⓘ
canonical problem for PCP-based hardness results ⓘ |
| usedFor |
demonstrating tight PCP theorems
ⓘ
reductions to other approximation problems ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Max-3-SAT Description of subject: Max-3-SAT is an optimization variant of the Boolean satisfiability problem where the goal is to maximize the number of satisfied clauses, each containing exactly three literals, and it serves as a central problem in the study of approximation algorithms and hardness of approximation.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
“Inapproximability results for SAT and other problems”
linked to: Max-3-SAT