Furst–Saxe–Sipser lower bounds
E518865
Furst–Saxe–Sipser lower bounds are foundational results in circuit complexity theory that established superpolynomial lower bounds for constant-depth Boolean circuits (AC⁰), demonstrating inherent limitations of such circuits for computing certain functions.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Furst–Saxe–Sipser lower bounds canonical | 1 |
| Parity, circuits, and the polynomial-time hierarchy | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5393014 — 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: Furst–Saxe–Sipser lower bounds Context triple: [Håstad’s switching lemma, relatedTo, Furst–Saxe–Sipser lower bounds]
-
A.
“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.
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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.
“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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D.
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.
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E.
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.
- 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: Furst–Saxe–Sipser lower bounds Target entity description: Furst–Saxe–Sipser lower bounds are foundational results in circuit complexity theory that established superpolynomial lower bounds for constant-depth Boolean circuits (AC⁰), demonstrating inherent limitations of such circuits for computing certain functions.
-
A.
“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.
-
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.
“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.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
circuit complexity lower bound
ⓘ
result in computational complexity theory ⓘ |
| appliesTo |
AC⁰ circuits
ⓘ
Boolean circuits ⓘ constant-depth circuits ⓘ |
| authors |
James B. Saxe
ⓘ
Merrick L. Furst ⓘ Michael Sipser ⓘ |
| complexityClassContext |
AC⁰
ⓘ
P ⓘ |
| consequence |
evidence of inherent limitations of shallow circuits
ⓘ
first superpolynomial lower bounds for natural circuit class ⓘ |
| depthRestriction | constant depth ⓘ |
| field |
circuit complexity
ⓘ
computational complexity theory ⓘ |
| gateType |
NOT gates
ⓘ
unbounded fan-in AND gates ⓘ unbounded fan-in OR gates ⓘ |
| historicalSignificance | among earliest strong lower bounds for explicit Boolean functions in a natural circuit model ⓘ |
| implies |
parity not in AC⁰
ⓘ
separation between AC⁰ and some functions in P ⓘ |
| influenced |
Håstad’s 1986 lower bounds
ⓘ
subsequent AC⁰ lower bound research ⓘ |
| isAbout | limitations of constant-depth polynomial-size circuits ⓘ |
| namedAfter |
James B. Saxe
ⓘ
Merrick Furst ⓘ Michael Sipser ⓘ |
| originalPaperTitle |
Parity, circuits, and the polynomial-time hierarchy
ⓘ
linked to:
Furst–Saxe–Sipser lower bounds
|
| provesLowerBoundFor |
MOD₂ function
ⓘ
parity function ⓘ |
| publishedIn | Journal of Computer and System Sciences ⓘ |
| relatedTo | polynomial-time hierarchy ⓘ |
| resultType | nontrivial circuit lower bound ⓘ |
| shows |
existence of functions not computable by polynomial-size constant-depth circuits
ⓘ
limitations of AC⁰ circuits ⓘ relativized separation results for the polynomial-time hierarchy ⓘ superpolynomial lower bounds for constant-depth Boolean circuits ⓘ |
| sizeRestriction | polynomial size ⓘ |
| strengthenedBy |
Håstad’s optimal AC⁰ lower bounds
ⓘ
Håstad’s switching lemma ⓘ |
| techniqueUsed |
random restrictions
ⓘ
switching lemma–style arguments precursor ⓘ |
| yearPublished | 1981 ⓘ |
How these facts were elicited
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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: Furst–Saxe–Sipser lower bounds Description of subject: Furst–Saxe–Sipser lower bounds are foundational results in circuit complexity theory that established superpolynomial lower bounds for constant-depth Boolean circuits (AC⁰), demonstrating inherent limitations of such circuits for computing certain functions.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
Furst–Saxe–Sipser lower bounds
→
originalPaperTitle
→
Parity, circuits, and the polynomial-time hierarchy
ⓘ
linked to: Furst–Saxe–Sipser lower bounds