Contemporary Definition
It is discussed in. It is extensively studied in where also the main properties are resolved. The Kolmogorov structure function can be written as
where x is a binary string of length n with where S is a contemplated model (set of n-length strings) for x, is the Kolmogorov complexity of S and is a nonnegative integer value bounding the complexity of the contemplated S's. Clearly, this function is nonincreasing and reaches for where c is the required number of bits to change x into and is the Kolmogorov complexity of x.
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