Editing Computability Theory (section)

== <span style="color: #FFFFFF;">Remembering</span> ==
* '''Computability Theory''' — The study of the mathematical limits of computation.
* '''Algorithm''' — A step-by-step procedure for solving a problem.
* '''Turing Machine''' — A theoretical model of a computer consisting of an infinite tape and a read/write head (The "Gold Standard" for what is computable).
* '''Decidability''' — A property of a problem that can be solved with a "Yes/No" answer by an algorithm in finite time.
* '''Recursively Enumerable''' — A set where a computer can list all the elements, but might never finish.
* '''The Halting Problem''' — The famous proof that you cannot write a program that can tell if ''any'' other program will eventually stop or run forever.
* '''Church-Turing Thesis''' — The hypothesis that any problem that can be solved by a "Human with a pencil" can be solved by a Turing Machine.
* '''P vs. NP''' — The most famous unsolved problem: "If a solution is easy to check, is it also easy to find?"
* '''Turing Completeness''' — A system is Turing Complete if it can simulate any Turing Machine (e.g., Python, C++, and even some video games like Minecraft).
* '''Undecidable Problem''' — A problem for which it is mathematically impossible to construct an algorithm that always leads to a correct yes-or-no answer.
* '''Oracle Machine''' — A theoretical computer that has access to a "Magic Box" that can solve one specific undecidable problem instantly.
* '''Rice's Theorem''' — A theorem stating that ''any'' non-trivial property of a program's behavior is undecidable.
* '''Busy Beaver''' — A game to find the simplest program that runs for the longest possible time before stopping.
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