Sophistication Revisited

Kolmogorov complexity measures the ammount of information in a string as the size of the shortest program that computes the string. The Kolmogorov structure function divides the smallest program producing a string in two parts: the useful information present in the string, called sophistication if based on total functions, and the remaining accidental information. We formalize a connection between sophistication (due to Koppel) and a variation of computational depth (intuitively the useful or nonrandom information in a string), prove the existence of strings with maximum sophistication and show that they are the deepest of all strings.

• Type: Conference
• Year: 2003
• Where: ICALP
• Authors: Luis Antunes 0002, Lance Fortnow
• Keywords: ICALP 2003, Kolmogorov Complexity, Kolmogorov Structure Function, String, Theoretical Computer Science