# Some Theorems on Incremental Compression

Conference paper

First Online:

## Abstract

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.

## Keywords

Incremental compression Data compression Algorithmic complexity Universal induction Universal search Feature extraction## Notes

### Acknowledgements

I would like to express my gratitude to Alexey Potapov and Alexander Priamikov for proof reading and helpful comments.

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