Automatic Complexity - A Computable Measure of Irregularity

Automatic Complexity discusses a treatment of a computable form of Kolmogorov complexity, in which Turing machines are replaced by finite automata. The complexities of many types of words are studied, including random words, normal words, Fibonacci words, Thue words, and words produced by linear feedback shift registers.

Automatic complexity is a computable and visual form of Kolmogorov complexity. Introduced by Shallit and Wang in 2001, it replaces Turing machines by finite automata, and has connections to normalized information distance, logical depth, and linear diophantine equations. Automatic Complexity is the first book on the subject and includes exercises with solutions written for the proof assistant Lean, computer programs to calculate automatic complexity, and many open problems.