Turing reducibility
E679186
Turing reducibility is a central computability-theoretic notion that compares the relative computational difficulty of decision problems by allowing one problem to be solved using an oracle for another.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Turing reducibility canonical | 2 |
| Turing reduction | 2 |
| Turing reductions | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7666829 — 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: Turing reducibility Context triple: [Computability Theory, fieldOfStudy, Turing reducibility]
-
A.
Computability Theory
Computability Theory is a branch of theoretical computer science and mathematical logic that studies which problems can be solved by algorithms and how efficiently they can be computed.
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B.
Karp reductions
Karp reductions are polynomial-time many-one reductions used in computational complexity theory to show that one decision problem is at least as hard as another, central to defining NP-completeness.
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C.
Rice's theorem
Rice's theorem is a fundamental result in computability theory stating that any non-trivial semantic property of the language recognized by a Turing machine is undecidable.
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D.
Church–Turing thesis
The Church–Turing thesis is a foundational principle in computability theory stating that any function that can be effectively computed by an algorithm can be computed by a Turing machine (or equivalently by other formal models of computation).
-
E.
Kolmogorov complexity
Kolmogorov complexity is a measure of the amount of information in an object, defined as the length of the shortest computer program that can produce it.
- 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: Turing reducibility Target entity description: Turing reducibility is a central computability-theoretic notion that compares the relative computational difficulty of decision problems by allowing one problem to be solved using an oracle for another.
-
A.
Computability Theory
Computability Theory is a branch of theoretical computer science and mathematical logic that studies which problems can be solved by algorithms and how efficiently they can be computed.
-
B.
Karp reductions
Karp reductions are polynomial-time many-one reductions used in computational complexity theory to show that one decision problem is at least as hard as another, central to defining NP-completeness.
-
C.
Rice's theorem
Rice's theorem is a fundamental result in computability theory stating that any non-trivial semantic property of the language recognized by a Turing machine is undecidable.
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D.
Church–Turing thesis
The Church–Turing thesis is a foundational principle in computability theory stating that any function that can be effectively computed by an algorithm can be computed by a Turing machine (or equivalently by other formal models of computation).
-
E.
Kolmogorov complexity
Kolmogorov complexity is a measure of the amount of information in an object, defined as the length of the shortest computer program that can produce it.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
computability-theoretic notion
ⓘ
reducibility notion ⓘ relative computability concept ⓘ |
| allows |
arbitrary adaptive oracle queries
ⓘ
unbounded number of oracle queries ⓘ |
| alsoKnownAs |
Turing reducibility relation
ⓘ
Turing reduction ⓘ
linked to:
Turing reducibility
|
| appliesTo |
decision problems
ⓘ
sets of integers ⓘ subsets of ω ⓘ |
| basedOn | oracle Turing machines ⓘ |
| captures |
relative computational difficulty
ⓘ
relative solvability of problems ⓘ |
| compares |
decision problems
ⓘ
languages over finite alphabets ⓘ sets of natural numbers ⓘ |
| definition | A is Turing reducible to B if A is decidable by a Turing machine with oracle for B ⓘ |
| equivalenceRelation | A ≡_T B iff A ≤_T B and B ≤_T A ⓘ |
| field |
computability theory
ⓘ
mathematical logic ⓘ theoretical computer science ⓘ
linked to:
Theoretical Computer Science
|
| formalCondition | A ≤_T B iff there exists an oracle Turing machine M^B that decides membership in A ⓘ |
| generalizes |
Turing computability without oracles
ⓘ
many-one reducibility ⓘ |
| historicalPeriod | 1930s ⓘ |
| implies | many-one reducibility implies Turing reducibility ⓘ |
| induces |
equivalence relation of Turing equivalence
ⓘ
preorder on sets of natural numbers ⓘ |
| isWeakerThan |
many-one reducibility
ⓘ
one-one reducibility ⓘ truth-table reducibility ⓘ |
| keyProperty |
not antisymmetric on all sets
ⓘ
reflexive on all sets ⓘ transitive on all sets ⓘ |
| originator | Alan Turing ⓘ |
| preserves | Turing computability ⓘ |
| relatedConcept |
Turing degree
ⓘ
linked to:
Turing degrees
many-one reducibility ⓘ oracle Turing machine ⓘ polynomial-time Turing reducibility ⓘ truth-table reducibility ⓘ weak truth-table reducibility ⓘ |
| symbol | ≤_T ⓘ |
| usedIn |
classification of unsolvable problems
ⓘ
degree theory ⓘ study of the analytical hierarchy ⓘ study of the arithmetical hierarchy ⓘ |
| usedToDefine |
Turing degrees
ⓘ
degree of unsolvability ⓘ relative computability hierarchy ⓘ |
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: Turing reducibility Description of subject: Turing reducibility is a central computability-theoretic notion that compares the relative computational difficulty of decision problems by allowing one problem to be solved using an oracle for another.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Turing reducibility
subject linked to:
Karp reductions
linked to: Turing reducibility
linked to: Turing reducibility