2008/09/15 by Luís Antunes, Armando B. Matos, Antunes, Luis +5
Computer Science · #Algorithms and Data Compression #Computability, Logic, AI Algorithms #Computational Complexity (cs.CC) #Evolutionary Algorithms and Applications #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.0809.2546
openalex publication_date 2008/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Depth of an object concerns a tradeoff between computation time and excess of program length over the shortest program length required to obtain the object. It gives an unconditional lower bound on the computation time from a given program in absence of auxiliary information. Variants known as logical depth and computational depth are expressed in Kolmogorov complexity theory. We derive quantitative relation between logical depth and computational depth and unify the different depth notions by relating them to A. Kolmogorov and L. Levin's fruitful notion of randomness deficiency. Subsequently, we revisit the computational depth of infinite strings, introducing the notion of super deep sequences and relate it with other approaches.