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Computability theory and Post's theorem

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Computability theory and Post's theorem

Computability theory vs. Post's theorem

Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. In computability theory Post's theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees.

Similarities between Computability theory and Post's theorem

Computability theory and Post's theorem have 11 things in common (in Unionpedia): Arithmetical hierarchy, Emil Leon Post, Halting problem, Many-one reduction, Oracle machine, Peano axioms, Recursively enumerable set, Turing degree, Turing jump, Turing machine, Turing reduction.

Arithmetical hierarchy

In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy classifies certain sets based on the complexity of formulas that define them.

Arithmetical hierarchy and Computability theory · Arithmetical hierarchy and Post's theorem · See more »

Emil Leon Post

Emil Leon Post (February 11, 1897 – April 21, 1954) was an American mathematician and logician.

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Halting problem

In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running (i.e., halt) or continue to run forever.

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Many-one reduction

In computability theory and computational complexity theory, a many-one reduction is a reduction which converts instances of one decision problem into instances of a second decision problem.

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Oracle machine

In complexity theory and computability theory, an oracle machine is an abstract machine used to study decision problems.

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Peano axioms

In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.

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Recursively enumerable set

In computability theory, traditionally called recursion theory, a set S of natural numbers is called recursively enumerable, computably enumerable, semidecidable, provable or Turing-recognizable if.

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Turing degree

In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures the level of algorithmic unsolvability of the set.

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Turing jump

In computability theory, the Turing jump or Turing jump operator, named for Alan Turing, is an operation that assigns to each decision problem a successively harder decision problem with the property that is not decidable by an oracle machine with an oracle for.

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Turing machine

A Turing machine is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules.

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Turing reduction

In computability theory, a Turing reduction from a problem A to a problem B, is a reduction which solves A, assuming the solution to B is already known (Rogers 1967, Soare 1987).

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The list above answers the following questions

Computability theory and Post's theorem Comparison

Computability theory has 101 relations, while Post's theorem has 21. As they have in common 11, the Jaccard index is 9.02% = 11 / (101 + 21).

References

This article shows the relationship between Computability theory and Post's theorem. To access each article from which the information was extracted, please visit:

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