Sophistication (complexity theory)

In algorithmic information theory, sophistication is a measure of complexity related to algorithmic entropy.

When K is the Kolmogorov complexity and c is a constant, the sophistication of x can be defined as[1]

The constant c is called significance. The S variable ranges over finite sets.

Intuitively, sophistication measures the complexity of a set of which the object is a "generic" member.

See also

References

  1. Mota, Francisco; Aaronson, Scott; Antunes, Luís; Souto, André. "Sophistication as Randomness Deficiency" (PDF). doi:10.1007/978-3-642-39310-5_17. Cite journal requires |journal= (help)

Further reading

  • Koppel, Moshe (1995). Herken, Rolf (ed.). "Structure". The Universal Turing Machine (2Nd Ed.). Springer-Verlag New York, Inc.: 403–419. ISBN 3-211-82637-8.
  • Antunes, Luís; Fortnow, Lance (August 30, 2007). "Sophistication Revisited" (PDF). doi:10.1007/s00224-007-9095-5. Cite journal requires |journal= (help)
  • Luís, Antunes; Bauwens, Bruno; Souto, André; Teixeira, Andreia (2013). "Sophistication vs Logical Depth". arXiv:1304.8046.


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