Computability theory and Many-one reduction

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Difference between Computability theory and Many-one reduction

Computability theory vs. Many-one reduction

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 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.

Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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Computable function

Computable functions are the basic objects of study in computability theory.

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Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

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Emil Leon Post

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

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Formal language

In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols together with a set of rules that are specific to it.

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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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Injective function

In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.

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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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Transactions of the American Mathematical Society

The Transactions of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.

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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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Universal Turing machine

In computer science, a universal Turing machine (UTM) is a Turing machine that can simulate an arbitrary Turing machine on arbitrary input.

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