“Inapproximability results for SAT and other problems”
E124291
“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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| “Inapproximability results for SAT and other problems” canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1043667 — 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: “Inapproximability results for SAT and other problems” Context triple: [Johan Håstad, notableWork, “Inapproximability results for SAT and other problems”]
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A.
Interactive Proofs and the Hardness of Approximating Cliques
"Interactive Proofs and the Hardness of Approximating Cliques" is a seminal theoretical computer science paper that introduced powerful interactive proof techniques to show that finding near-maximum cliques in graphs is computationally intractable to approximate within strong bounds.
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B.
Håstad’s switching lemma
Håstad’s switching lemma is a fundamental result in computational complexity theory that provides powerful bounds on the simplification of Boolean formulas under random restrictions, with major applications in circuit lower bounds.
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C.
PCP theorem
The PCP theorem is a fundamental result in computational complexity theory stating that every problem in NP has probabilistically checkable proofs that can be verified by examining only a constant number of bits, with major implications for the hardness of approximation.
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D.
“Almost optimal lower bounds for small depth circuits”
“Almost optimal lower bounds for small depth circuits” is a seminal theoretical computer science paper by Johan Håstad that establishes near-tight lower bounds on the size of constant-depth Boolean circuits, profoundly influencing circuit complexity theory.
-
E.
Blum complexity measures
Blum complexity measures are a formal framework in computational complexity theory that rigorously define and compare the resource usage (such as time or space) of algorithms via axiomatic conditions.
- 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: “Inapproximability results for SAT and other problems” Target entity description: “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.
-
A.
Interactive Proofs and the Hardness of Approximating Cliques
"Interactive Proofs and the Hardness of Approximating Cliques" is a seminal theoretical computer science paper that introduced powerful interactive proof techniques to show that finding near-maximum cliques in graphs is computationally intractable to approximate within strong bounds.
-
B.
Håstad’s switching lemma
Håstad’s switching lemma is a fundamental result in computational complexity theory that provides powerful bounds on the simplification of Boolean formulas under random restrictions, with major applications in circuit lower bounds.
-
C.
PCP theorem
The PCP theorem is a fundamental result in computational complexity theory stating that every problem in NP has probabilistically checkable proofs that can be verified by examining only a constant number of bits, with major implications for the hardness of approximation.
-
D.
“Almost optimal lower bounds for small depth circuits”
“Almost optimal lower bounds for small depth circuits” is a seminal theoretical computer science paper by Johan Håstad that establishes near-tight lower bounds on the size of constant-depth Boolean circuits, profoundly influencing circuit complexity theory.
-
E.
Blum complexity measures
Blum complexity measures are a formal framework in computational complexity theory that rigorously define and compare the resource usage (such as time or space) of algorithms via axiomatic conditions.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
scientific paper
ⓘ
theoretical computer science paper ⓘ |
| area |
complexity of Boolean satisfiability
ⓘ
optimization versions of NP-complete problems ⓘ |
| author | Johan Håstad ⓘ |
| authorAffiliation |
KTH Royal Institute of Technology
ⓘ
surface form:
Royal Institute of Technology (KTH)
|
| authorCitizenship | Sweden ⓘ |
| basedOn |
NP ≠ P assumption
ⓘ
PCP framework ⓘ |
| citationRole | highly cited work in theoretical computer science ⓘ |
| contribution |
establishes tight hardness-of-approximation bounds for SAT
ⓘ
establishes tight hardness-of-approximation bounds for related optimization problems ⓘ shows optimal inapproximability for Max-3-SAT under standard complexity assumptions ⓘ shows optimal inapproximability for Max-E3-LIN-2 under standard complexity assumptions ⓘ uses probabilistically checkable proofs to derive inapproximability results ⓘ |
| establishes | tight inapproximability thresholds for several optimization problems ⓘ |
| field |
approximation algorithms
ⓘ
Complexity Theory ⓘ
surface form:
computational complexity theory
hardness of approximation ⓘ theoretical computer science ⓘ |
| impact |
provided benchmarks for approximation algorithm performance
ⓘ
shaped the modern theory of hardness of approximation ⓘ |
| influencedBy |
PCP theorem
ⓘ
earlier work on hardness of approximation ⓘ |
| influencedField |
complexity of constraint satisfaction problems
ⓘ
design of approximation algorithms ⓘ |
| language | English ⓘ |
| method |
PCP constructions with few queries
ⓘ
gap amplification ⓘ |
| notableFor |
being a seminal paper in hardness of approximation
ⓘ
providing optimal inapproximability results for several classic NP-optimization problems ⓘ |
| relatedConcept |
Max-3-SAT
ⓘ
Max-E3-LIN-2 ⓘ Max-SAT ⓘ gap-introducing reductions ⓘ |
| researchArea |
PCP-based reductions
ⓘ
complexity of approximation problems ⓘ |
| resultType | hardness of approximation ⓘ |
| shows |
certain approximation ratios for SAT are NP-hard to achieve
ⓘ
improving beyond specific approximation factors for some problems would imply P = NP ⓘ |
| topic |
NP-hardness of approximation
ⓘ
PCP theorem ⓘ constraint satisfaction problems ⓘ probabilistically checkable proofs ⓘ satisfiability problem ⓘ |
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: “Inapproximability results for SAT and other problems” Description of subject: “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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.