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What (who) is computability theory - definition

STUDY OF COMPUTABLE FUNCTIONS AND TURING DEGREES

Computability Theory; Computability theory (computation); Ecursion theory; Theory of computability; Recursion theory; Computability theory (computer science); Continuous computability theory; Turing computability

computability theory

<mathematics> The area of theoretical computer science concerning what problems can be solved by any computer. A function is computable if an algorithm can be implemented which will give the correct output for any valid input. Since computer programs are countable but real numbers are not, it follows that there must exist real numbers that cannot be calculated by any program. Unfortunately, by definition, there isn't an easy way of describing any of them! In fact, there are many tasks (not just calculating real numbers) that computers cannot perform. The most well-known is the halting problem, the busy beaver problem is less famous but just as fascinating. ["Computability", N.J. Cutland. (A well written undergraduate-level introduction to the subject)]. ["The Turing Omnibus", A.K. Dewdeney]. (1995-01-13)

Computability theory

Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability.

https://en.wikipedia.org/wiki/Computability_theory

recursion theory

<theory> The study of problems that, in principle, cannot be solved by either computers or humans. [Proper definition?] (1999-03-01)

Wikipedia

Computability theory

Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability. In these areas, computability theory overlaps with proof theory and effective descriptive set theory.

Basic questions addressed by computability theory include:

What does it mean for a function on the natural numbers to be computable?
How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?

Although there is considerable overlap in terms of knowledge and methods, mathematical computability theorists study the theory of relative computability, reducibility notions, and degree structures; those in the computer science field focus on the theory of subrecursive hierarchies, formal methods, and formal languages.

https://en.wikipedia.org/wiki/Computability theory