A Survey on Complexity Measures for Pseudo-Random Sequences

Abstract

Since the introduction of the Kolmogorov complexity of binary sequences in the 1960s, there have been significant advancements on the topic of complexity measures for randomness assessment, which are of fundamental importance in theoretical computer science and of practical interest in cryptography. This survey reviews notable research from the past four decades on the linear, quadratic and maximum-order complexities of pseudo-random sequences, and their relations with Lempel–Ziv complexity, expansion complexity, 2-adic complexity and correlation measures.