If my understanding is correct, Kolmogorov complexity would assign the highest value (description length) to a totally random string, such as:
the lowest value to a completely regular string, such as:
and a middle value to:
But it seems to me that although the 1st string cannot be perfectly described by any string shorter than itself, it can be more less characterized by a random distribution, i.e. its lack of any structure makes it in a sense less complex than the 3rd string.
Is there any information theoretic or algorithmic measure of complexity that would assign low values to the 1st and 2nd strings while assigning a high value to the 3rd string and strings that have long description length, but do display some structure and regularity?