semiavgörbara

semiavgörbara is a term used in mathematics, specifically in the field of computability theory. It refers to a type of problem or statement for which an algorithm can be devised that will either halt and provide a definitive "yes" or "no" answer, or it will run forever. This is in contrast to a decidable problem, for which an algorithm must always halt and provide a correct answer.

The concept of semi-decidability is closely linked to the Halting Problem, which is a famous example of a problem that is not decidable, but is semi-decidable. For the Halting Problem, an algorithm can determine if a given program will halt on a given input, but it cannot definitively say that a program will *not* halt. If the algorithm halts, it correctly answers "yes." If the program it is analyzing runs forever, the halting problem algorithm will also run forever, thus demonstrating its semi-decidable nature.

Semi-decidable problems are also known as recursively enumerable problems. This terminology arises from the fact that the set of inputs for which a semi-decidable problem yields a "yes" answer can be enumerated by a Turing machine. The existence of semi-decidable problems is a fundamental result in computability theory, highlighting the inherent limitations of what can be computed by algorithms. Understanding semi-decidability is crucial for grasping the boundaries of algorithmic computation and the nature of undecidable problems.