Ákvarðanlegur

Ákvarðanlegur is an Icelandic word that translates to "decidable" in English, commonly used in the context of logic and computer science. A problem or a question is considered ákvarðanlegur if there exists an algorithm that can determine, in a finite amount of time, whether the answer to the problem is yes or no. This is a fundamental concept in computability theory, which explores the limits of what can be computed by algorithms.

The idea of decidability is closely related to the concept of an algorithm. For a problem to be decidable, not only must there be a correct answer, but there must also be a systematic procedure that guarantees finding that answer for any given input. If no such algorithm exists, the problem is deemed "ákvarðanlegur ekki" or undecidable.

Many fundamental problems in mathematics and computer science have been proven to be undecidable. For instance, the halting problem, which asks whether an arbitrary program will eventually finish or run forever, is a famous example of an undecidable problem. Understanding which problems are decidable and which are not is crucial for designing efficient algorithms and for understanding the theoretical boundaries of computation. The term is used to categorize problems based on their inherent computational complexity and solvability.