Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Vereshchagin, N., Vitányi, P.: Kolmogorov’s structure functions and model selection. IEEE Transactions on Information Theory 50(12), 3265–3290 (2004)
Li, M., Vitányi, P.: An introduction to Kolmogorov complexity and its applications, 3rd edn. Springer (2008)
Gács, P.: On the symmetry of algorithmic information. Soviet Mathematics Doklady 15, 1477–1480 (1974)
Koppel, M.: Structure. In: Herken, R. (ed.) The Universal Turing Machine: A Half-Century Survey, pp. 435–452. Oxford University Press (1988)
Vitányi, P.: Meaningful information. IEEE Transactions on Information Theory 52(10), 4617–4626 (2006)
Antunes, L., Fortnow, L.: Sophistication revisited. Theory of Computing Systems 45(1), 150–161 (2009)
Aaronson, S.: Can a string’s sophistiocation be defined in an unsophisticated way? (2012), http://mathoverflow.net/questions/103619
Antunes, L., Matos, A., Souto, A., Vitányi, P.: Depth as randomness deficiency. Theory of Computing Systems 45(4), 724–739 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mota, F., Aaronson, S., Antunes, L., Souto, A. (2013). Sophistication as Randomness Deficiency. In: Jurgensen, H., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2013. Lecture Notes in Computer Science, vol 8031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39310-5_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-39310-5_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39309-9
Online ISBN: 978-3-642-39310-5
eBook Packages: Computer ScienceComputer Science (R0)