The descriptive complexity of strings
The descriptive complexity of strings
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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