Automatic complexity : a computable measure of irregularity / Bjørn Kjos-Hanssen.

Format:

Book

Author/Creator:

Kjos-Hanssen, Bjørn, author.

Series:

De Gruyter series in logic and its applications series

De Gruyter series in logic and its applications series ; v.12

Language:

English

Subjects (All):

Computational complexity.

Information theory.

Physical Description:

1 online resource (156 pages)

Edition:

1st ed.

Place of Publication:

Berlin/Boston : Walter de Gruyter GmbH, [2024]

Summary:

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.

Contents:

Intro

Preface

Acknowledgments

Contents

1 First steps in automatic complexity

2 Nondeterminism and overlap-free words

3 Edge complexity and digraphs

4 The many variants

5 The incompressibility theorem

6 Conditional automatic complexity

7 Logical depth and automatic complexity

Bibliography

Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-11-077487-9

OCLC:

1416301418