ákvarðanleg

ákvarðanleg is an Icelandic word that translates to "decidable" in English. It is a term primarily used in the field of computer science and theoretical computer science, particularly within mathematical logic and computability theory.

A problem or a statement is considered ákvarðanleg if there exists an algorithm that can, for any given input, determine in a finite amount of time whether the input satisfies the problem's conditions or whether the statement is true. This means that there is a mechanical procedure that will always halt and provide a correct yes/no answer.

The concept of decidability is fundamental to understanding the limits of computation. Not all problems are decidable. For example, the Halting Problem, which asks whether an arbitrary program will eventually halt or run forever, has been proven to be undecidable. This means no general algorithm can solve it for all possible programs.

In essence, ákvarðanleg describes problems that are algorithmically solvable. The study of decidability helps differentiate between what can and cannot be computed, influencing the design and theoretical underpinnings of computer systems and algorithms. It is a core concept for understanding the boundaries of what computers can achieve.