Computability Theory

E173643

academic discipline subfield of mathematical logic subfield of theoretical computer science

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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All labels observed (3)

Label	Occurrences
Turing computability	4
Computability Theory canonical	2
recursion theory	2

How this entity was disambiguated

This entity first appeared as the object of triple T1531824 — 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: Computability Theory
Context triple: [Introduction to the Theory of Computation, hasSection, Computability Theory]

A. Introduction to the Theory of Computation
Introduction to the Theory of Computation is a widely used textbook in theoretical computer science that covers formal languages, automata, computability, and complexity theory.
B. 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).
C. Mathematics and Computation
"Mathematics and Computation" is a book by Avi Wigderson that explores the deep connections between theoretical computer science and mathematics, emphasizing how computational complexity shapes modern mathematical thought.
D. On Computable Numbers with an Application to the Entscheidungsproblem
"On Computable Numbers, with an Application to the Entscheidungsproblem" is Alan Turing’s landmark 1936 paper that introduced the Turing machine model and founded the formal study of computability and the limits of algorithmic decision procedures.
E. Computational Complexity: A Conceptual Perspective
Computational Complexity: A Conceptual Perspective is a graduate-level textbook that presents the foundations and key themes of computational complexity theory with an emphasis on conceptual understanding over technical detail.
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: Computability Theory
Target entity description: 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.

A. Introduction to the Theory of Computation
Introduction to the Theory of Computation is a widely used textbook in theoretical computer science that covers formal languages, automata, computability, and complexity theory.
B. 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).
C. Mathematics and Computation
"Mathematics and Computation" is a book by Avi Wigderson that explores the deep connections between theoretical computer science and mathematics, emphasizing how computational complexity shapes modern mathematical thought.
D. On Computable Numbers with an Application to the Entscheidungsproblem
"On Computable Numbers, with an Application to the Entscheidungsproblem" is Alan Turing’s landmark 1936 paper that introduced the Turing machine model and founded the formal study of computability and the limits of algorithmic decision procedures.
E. Computational Complexity: A Conceptual Perspective
Computational Complexity: A Conceptual Perspective is a graduate-level textbook that presents the foundations and key themes of computational complexity theory with an emphasis on conceptual understanding over technical detail.
F. None of above. chosen

Statements (54)

Predicate	Object
instanceOf	academic discipline ⓘ subfield of mathematical logic ⓘ subfield of theoretical computer science ⓘ
basedOn	discrete mathematics ⓘ formal logic ⓘ
fieldOfStudy	Church–Turing thesis ⓘ Gödel numbering ⓘ Kolmogorov complexity ⓘ Post correspondence problem ⓘ Rice's theorem ⓘ Turing degrees ⓘ Turing machines ⓘ linked to: Turing machine Turing reducibility ⓘ algorithmic randomness ⓘ algorithmic solvability ⓘ analytical hierarchy ⓘ arithmetical hierarchy ⓘ computability ⓘ computable analysis ⓘ computable functions ⓘ computable structures ⓘ computably enumerable sets ⓘ decidability ⓘ decision problems ⓘ degrees of unsolvability ⓘ effective enumerations ⓘ effective procedures ⓘ halting problem ⓘ many-one reducibility ⓘ non-computable functions ⓘ oracle machines ⓘ partial recursive functions ⓘ primitive recursive functions ⓘ recursion theorem ⓘ recursive functions ⓘ recursive sets ⓘ recursively enumerable sets ⓘ relative computability ⓘ reverse mathematics ⓘ semi-decidable problems ⓘ undecidable problems ⓘ
hasKeyFigure	Alan Turing ⓘ Alonzo Church ⓘ Emil Post ⓘ Kurt Gödel ⓘ Stephen Kleene ⓘ
relatedTo	complexity theory ⓘ proof theory ⓘ set theory ⓘ
studies	classification of problems by computability ⓘ formal models of computation ⓘ limits of algorithmic computation ⓘ relationships between different models of computation ⓘ which problems can be solved by algorithms ⓘ

How these facts were elicited