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 (1)
| Label | Occurrences |
|---|---|
| Furst–Saxe–Sipser lower bounds canonical | 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]
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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
NERFINISHED
ⓘ
Merrick L. Furst NERFINISHED ⓘ Michael Sipser NERFINISHED ⓘ |
| complexityClassContext |
AC⁰
NERFINISHED
ⓘ
P NERFINISHED ⓘ |
| 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
NERFINISHED
ⓘ
Merrick Furst NERFINISHED ⓘ Michael Sipser NERFINISHED ⓘ |
| originalPaperTitle | Parity, circuits, and the polynomial-time hierarchy NERFINISHED ⓘ |
| provesLowerBoundFor |
MOD₂ function
ⓘ
parity function ⓘ |
| publishedIn | Journal of Computer and System Sciences NERFINISHED ⓘ |
| 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
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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 (1)
Full triples — surface form annotated when it differs from this entity's canonical label.