Kolmogorov structure functions for automatic complexity
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Bjørn Kjos-Hanssen
Department of Mathematics, University of Hawaii at Manoa
Probability Seminar, Smith Hall 102, 2:30pm, June 1, 2015, U. Washington
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.
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.
