Computabilitási

Computabilitási refers to the study of what problems can be solved by algorithms. It is a fundamental concept in theoretical computer science and mathematical logic. At its core, computability theory explores the limits of computation, asking whether a given problem can be solved by a mechanical procedure, or algorithm, regardless of the time or resources required.

The concept of an algorithm is often formalized using models of computation such as the Turing machine. A problem is considered computable if there exists a Turing machine that can solve it for all possible inputs. Problems that are not computable are called undecidable. The most famous example of an undecidable problem is the halting problem, which asks whether an arbitrary program will eventually halt or run forever on a given input.

Computability theory has profound implications for mathematics, computer science, and artificial intelligence. It provides a theoretical framework for understanding the capabilities and limitations of computers and forms the basis for many areas of computer science, including algorithm design, complexity theory, and formal verification. The study of computability helps define what is theoretically possible to compute and what is not.