The sophistication of a string measures how much structural information it contains. We introduce naive sophistication, a variant of sophistication based on randomness deficiency. Naive sophistication measures the minimum number of bits needed to specify a set in which the string is a typical element. Thanks to Vereshchagin and Vitányi, we know that sophistication and naive sophistication are equivalent up to low order terms. We use this to relate sophistication to lossy compression, and to derive an alternative formulation for busy beaver computational depth. © 2013 Springer-Verlag.
CITATION STYLE
Mota, F., Aaronson, S., Antunes, L., & Souto, A. (2013). Sophistication as randomness deficiency. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8031 LNCS, pp. 172–181). https://doi.org/10.1007/978-3-642-39310-5_17
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