Kolmogorov Structure Functions for Automatic Complexity in Computational Statistics

For a finite word w of length n and a class of finite automata A, we study the Kolmogorov structure function hw for automatic complexity restricted to A. We propose an approach to computational statistics based on the minimum p-value of hw(m) over 0 ≤ m ≤ n. When A is the class of all finite automata we give some upper bounds for hw. When A consists of automata that detect several success runs in w, we give efficient algorithms to compute hw. When A consists of automata that detect one success run, we moreover give an efficient algorithm to compute the p-values.