# Why study computational theory

## Computational theory

*Algorithm theory*, *Computability theory*, mathematical theory that deals with the formal concept of computability and algorithms.

The task of finding an adequate definition for "calculable" is considered to have been solved on the basis of Church's thesis, since all of the previously proposed concepts of calculability have turned out to be mutually equivalent (Turing machine). The formalization of the concept of calculation has turned out to be necessary after the prevailing idea around 1900 that all of mathematics can be algorithmized in a certain way. This idea was nullified by GĂ¶del's incompleteness theorem in 1931, which is located on the border between mathematical logic and computational theory. This sentence made it clear that there are non-calculable functions or non-decidable problems.

Examples of this are the undecidability of predicate logic (undecidable theory), the holding problem, the domino problem, the Post's correspondence problem, the tenth Hilbert's problem and the word problem for semi-Thue systems.

The advanced computational theory is concerned with, inter alia. with relative predictability and Turing reducibility, which can be defined using so-called oracle-Turing machines. In this way, hierarchies, such as the arithmetic hierarchy, can be considered within the non-decidable sets, and problems that are mutually Turing-reducible can be combined into equivalence classes, so-called Turing degrees. In the theory of the degrees of unsolvability, their association-theoretical structures are examined in particular.

Particular attention is also paid to the structure of the recursively enumerable sets.

A particularly successful proof technique for the construction of sets which on the one hand should receive desired properties and on the other hand should avoid other properties is the priority method.

- What is it like to live in Sweden?
- How can we define bad behavior
- What are the best lats exercises for body weight
- How did you prepare for vocabulary
- What is the most common smiley emoticon
- How do my upvotes on Quora sink?
- Who are the top developers of Node js
- How does MobiKwik make money
- How long has Quora been around?
- Why don't intelligent teachers make money?
- When was Uber founded?
- Why does everyone have long-distance relationships
- Does the tinting of windows really work?
- What are the worst grades at Cornell
- Are whole body exercises better for bodybuilding
- What are inelastic collisions in physics
- Why do professors advise against writing survey papers
- What is your opinion on Dave Ramsey
- What is the best way to invest 2k
- Who created the first Instagram account
- Why do Palestinians execute homosexuals
- Trimming makes the beard grow quickly
- IIT is a government
- What is the transport layer