  The algorithmic complexity of a bit string is a measure of how much a given bit string can be compressed by a computer. A long, but algorithmically simple, bit string can be compressed into a much shorter bit string. This shorter bit string could apparently be reset to zero, by resetting each individual bit, for a much lower cost than resetting each individual bit in the original longer bit string. A clever demon might, therefore, be able to compress its memory and so avoid the full erasure cost that would be needed to ensure a modified second law holds.