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André Nies

Print publication date: 2009

Print ISBN-13: 9780199230761

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780199230761.001.0001

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The descriptive complexity of strings

The descriptive complexity of strings

Chapter:
(p.74) 2 The descriptive complexity of strings
Source:
Computability and Randomness
Author(s):

André Nies

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199230761.003.0002

This chapter develops the theory of plain Kolmogorov complexity, and then of prefix-free Kolmogorov complexity. A main technical tool for later chapters is the Machine Existence (or Kraft–Chaitin) Theorem. The chapter uses some probability theory to obtain statistical properties of incompressible strings.

Keywords:   Kolmogorov complexity, prefix freeness, Machine Existence Theorem, Kraft–Chaitin, incompressibility

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