# A report on Computability theory, Formal language and Computer science

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.

- Computability theoryIn logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules.

- Formal languageAlthough 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.

- Computability theoryTherefore, formal language theory is a major application area of computability theory and complexity theory.

- Formal languageIn an effort to answer the first question, computability theory examines which computational problems are solvable on various theoretical models of computation.

- Computer scienceFormal methods are best described as the application of a fairly broad variety of theoretical computer science fundamentals, in particular logic calculi, formal languages, automata theory, and program semantics, but also type systems and algebraic data types to problems in software and hardware specification and verification.

- Computer science1 related topic with Alpha

## Mathematical logic

0 linksStudy of formal logic within mathematics.

Study of formal logic within mathematics.

Major subareas include model theory, proof theory, set theory, and recursion theory.

These systems, though they differ in many details, share the common property of considering only expressions in a fixed formal language.

Computer scientists often focus on concrete programming languages and feasible computability, while researchers in mathematical logic often focus on computability as a theoretical concept and on noncomputability.