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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]

{\displaystyle \operatorname {Soph} _{c}(x):=\inf\{\operatorname {K} (S):x\in S\land \operatorname {K} (x\mid S)\geq \log _{2}(|S|)-c\land |S|\in \mathbb {N} _{+}\}.}

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.

  1. ↑ Mota, Francisco; Aaronson, Scott; Antunes, Luís; Souto, André (2013). "Sophistication as Randomness Deficiency". Descriptional Complexity of Formal Systems. Lecture Notes in Computer Science. Vol. 8031. pp. 172–181. doi:10.1007/978-3-642-39310-5_17. ISBN 978-3-642-39309-9.