Suffix trees and string complexity

Abstract

Let s = (s1, s2, …, sn) be a sequence of characters where si ∈ Zp for 1 ≤ i ≤ n. One measure of the complexity of the sequence s is the length of the shortest feedback shift register that will generate s, which is known as the maximum order complexity of s [17, 18]. We provide a proof that the expected length of the shortest feedback register to generate a sequence of length n is less than 2 logp n + o(1), and also give several other statistics of interest for distinguishing random strings. The proof is based on relating the maximum order complexity to a data structure known as a suffix tree.