halbäquivalenz

Halbäquivalenz is a term used in theoretical computer science and logic to describe a specific relationship between two computational problems or statements. It signifies that one problem can be transformed into another problem in such a way that a solution to the second problem can be used to solve the first problem, but the transformation is not necessarily reversible. This is in contrast to full equivalence, where the transformation can be done in both directions.

More formally, problem A is said to be half-equivalent to problem B if there exists a computable function that transforms any instance of problem A into an instance of problem B, such that a solution to the transformed instance of B provides a solution to the original instance of A. However, there might not exist a similar computable function that transforms instances of B back into instances of A while preserving solvability.

The concept of half-equivalence is particularly relevant in the study of computational complexity and the classification of problems. For instance, in the context of reducibility, if problem A can be reduced to problem B (meaning A is no harder than B), and this reduction is one-way (a true "half-equivalence"), it implies that if B is decidable or solvable in a certain complexity class, then A is also decidable or solvable in a related complexity class. This allows for the transfer of complexity properties from one problem to another. It's a weaker form of equivalence that still provides valuable insights into the inherent difficulty of computational tasks.