structural:summarization, information:classification
Alternative definitions

There are many alternative definitions to the one presented above. Many of these are specialized for the case where the oracle solves a decision problem. In this case:

These definitions are equivalent from the point of view of Turing computability: a function is oracle-computable from a given oracle under all of these definitions if it is oracle-computable under any of them. The definitions are not equivalent, however, from the point of view of computational complexity. A definition such as the one by van Melkebeek, using an oracle tape which may have its own alphabet, is required in general.