Kolmogorov structure functions

for automatic complexity

Bjørn Kjos-Hanssen

Department of Mathematics, University of Hawaii at Manoa

Probability Seminar, Smith Hall 102, 2:30pm, June 1, 2015, U. Washington

Example

Pictured: a finite state automaton which only accepts one string of length 22, namely 0100011001010101111100, and which has 10 states. We say that this automaton is a witness to the fact that the string 0100011001010101111100 has automatic complexity at most 10.

Application: Statistics

The most statistically significant fact about a string such as 0000000010000000100, from an automatic point of view, may be the fact that it contains exactly two 1s. 

The precise number of 0s that occurs may be relatively insignificant. The theory of structure functions makes this intuitive idea precise.