Some Theorems on Incremental Compression

The ability to induce short descriptions of, i.e. compressing, a wide class of data is essential for any system exhibiting general intelligence. In all generality, it is proven that incremental compression – extracting features of data strings and continuing to compress the residual data variance – leads to a time complexity superior to universal search if the strings are incrementally compressible. It is further shown that such a procedure breaks up the shortest description into a set of pairwise orthogonal features in terms of algorithmic information.