Blum axioms
E117701
Blum axioms are a set of formal conditions introduced by Manuel Blum that rigorously define what constitutes a valid complexity measure in computational complexity theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Blum axioms canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T990924 — 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: Blum axioms Context triple: [Manuel Blum, notableWork, Blum axioms]
-
A.
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.
-
B.
Shannon–Khinchin axioms
The Shannon–Khinchin axioms are a set of fundamental conditions that uniquely characterize Shannon entropy as the standard measure of information and uncertainty in probability theory and information theory.
-
C.
Hilbert’s program
Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
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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.
-
E.
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two fundamental results in mathematical logic showing that any sufficiently powerful, consistent formal system cannot prove all true statements about arithmetic, and cannot prove its own consistency.
- 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: Blum axioms Target entity description: Blum axioms are a set of formal conditions introduced by Manuel Blum that rigorously define what constitutes a valid complexity measure in computational complexity theory.
-
A.
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.
-
B.
Shannon–Khinchin axioms
The Shannon–Khinchin axioms are a set of fundamental conditions that uniquely characterize Shannon entropy as the standard measure of information and uncertainty in probability theory and information theory.
-
C.
Hilbert’s program
Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
-
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.
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two fundamental results in mathematical logic showing that any sufficiently powerful, consistent formal system cannot prove all true statements about arithmetic, and cannot prove its own consistency.
- F. None of above. chosen
Statements (35)
| Predicate | Object |
|---|---|
| instanceOf |
axiom system
ⓘ
formal condition set ⓘ |
| appliesTo |
partial computable functions
ⓘ
programs ⓘ |
| areaOfApplication |
recursion theory
ⓘ
theory of computation ⓘ |
| assumes | effective enumeration of partial computable functions ⓘ |
| characterizes | admissible complexity measures ⓘ |
| definesConcept |
Blum complexity measures
ⓘ
surface form:
Blum complexity measure
|
| field | computational complexity theory ⓘ |
| formalizes | machine-independent complexity theory ⓘ |
| hasComponent |
axiom of decidability of bounded complexity set
ⓘ
axiom of definedness of the measure ⓘ |
| implies |
existence of complexity-theoretic hierarchies
ⓘ
invariance under choice of reasonable machine model ⓘ speed-up theorems for some measures ⓘ |
| influenced | machine-independent complexity theory ⓘ |
| introducedBy | Manuel Blum ⓘ |
| language | mathematical logic ⓘ |
| namedAfter | Manuel Blum ⓘ |
| publicationType | journal article ⓘ |
| publishedIn |
Blum complexity measures
ⓘ
surface form:
A Machine-Independent Theory of the Complexity of Recursive Functions
|
| publishedInJournal | Journal of the ACM ⓘ |
| purpose | to define valid complexity measures ⓘ |
| relatedConcept |
Kolmogorov complexity
ⓘ
space-constructible function ⓘ time-constructible function ⓘ |
| requires |
complexity measure is a partial computable function
ⓘ
complexity measure is defined on pairs of programs and inputs ⓘ domain of the complexity measure equals the domain of the computed function ⓘ the set of triples (program,input,bound) with complexity below the bound is decidable ⓘ |
| usedFor |
defining general complexity measures
ⓘ
defining space complexity ⓘ defining time complexity ⓘ |
| yearIntroduced | 1967 ⓘ |
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: Blum axioms Description of subject: Blum axioms are a set of formal conditions introduced by Manuel Blum that rigorously define what constitutes a valid complexity measure in computational complexity theory.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.