“Almost optimal lower bounds for small depth circuits”
E120580
“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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Håstad’s optimal lower bounds for small-depth circuits | 1 |
| “Almost optimal lower bounds for small depth circuits” canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1043666 — 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: “Almost optimal lower bounds for small depth circuits” Context triple: [Johan Håstad, notableWork, “Almost optimal lower bounds for small depth circuits”]
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A.
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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B.
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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C.
The Knowledge Complexity of Interactive Proof Systems
"The Knowledge Complexity of Interactive Proof Systems" is a seminal theoretical computer science paper that introduced the notion of zero-knowledge proofs, fundamentally shaping modern cryptography and complexity theory.
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D.
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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E.
Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing
Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing is a 1985 ACM conference volume collecting influential research papers in theoretical computer science, including foundational work on topics such as interactive proof systems and computational complexity.
- 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: “Almost optimal lower bounds for small depth circuits” Target entity description: “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.
-
A.
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.
-
B.
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.
-
C.
The Knowledge Complexity of Interactive Proof Systems
"The Knowledge Complexity of Interactive Proof Systems" is a seminal theoretical computer science paper that introduced the notion of zero-knowledge proofs, fundamentally shaping modern cryptography and complexity theory.
-
D.
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.
-
E.
Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing
Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing is a 1985 ACM conference volume collecting influential research papers in theoretical computer science, including foundational work on topics such as interactive proof systems and computational complexity.
- F. None of above. chosen
Statements (39)
| Predicate | Object |
|---|---|
| instanceOf |
scientific paper
ⓘ
theoretical computer science paper ⓘ |
| author | Johan Håstad ⓘ |
| authorAffiliationAtTime | Johan Håstad ⓘ |
| citedBy | many later works in complexity theory ⓘ |
| contribution |
establishes almost optimal lower bounds on the size of constant-depth Boolean circuits
ⓘ
introduces and develops powerful switching-lemma based techniques ⓘ shows strong lower bounds for AC0 circuits computing parity ⓘ |
| field |
circuit complexity
ⓘ
computational complexity theory ⓘ theoretical computer science ⓘ |
| focusesOn |
constant-depth Boolean circuits
ⓘ
near-tight lower bounds ⓘ small depth circuits ⓘ |
| hasAuthorNationality | Swedish ⓘ |
| impact |
became a standard reference for AC0 lower bounds
ⓘ
profoundly influenced circuit complexity theory ⓘ |
| influenced |
development of circuit complexity theory
ⓘ
lower bounds for formula size and depth ⓘ research on AC0 lower bounds ⓘ subsequent work on pseudorandomness and derandomization ⓘ |
| knownFor |
being a seminal result in circuit complexity
ⓘ
establishing strong limitations of AC0 circuits ⓘ near-tight size lower bounds for constant-depth circuits computing parity ⓘ |
| language | English ⓘ |
| mainTopic |
AC0 circuits
ⓘ
circuit size lower bounds ⓘ constant-depth circuits ⓘ lower bounds for Boolean circuits ⓘ |
| relatedTo |
Håstad’s switching lemma
ⓘ
surface form:
Håstad switching lemma
hardness versus randomness paradigm ⓘ lower bounds for formula depth ⓘ pseudorandom generators for AC0 ⓘ |
| resultOn |
majority function
ⓘ
parity function ⓘ |
| shows |
any constant-depth AC0 circuit computing parity requires superpolynomial size
ⓘ
lower bounds that are close to optimal up to polynomial factors ⓘ |
| usesMethod |
random restrictions
ⓘ
switching lemma ⓘ |
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: “Almost optimal lower bounds for small depth circuits” Description of subject: “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.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Håstad’s optimal lower bounds for small-depth circuits