An analytic upper bound on T-complexity

Abstract

The Titchener T-complexity CT of a string has applications in, e.g., randomness testing, event detection and similarity comparison. Like the Lempel-Ziv production complexity, the upper bound of CT is demonstrably not a linear function of the string length. Knowledge of the bound for a given length is however required in order to convert CT into a measure with linear upper bound such as Titchener's T-information. For this reason, the upper bound of CT has been investigated before by several authors, with various asymptotic solutions proposed. We present a new analytic closed-form asymptotic upper bound for CT based on the Hurwitz-Lerch zeta function.