An analytic upper bound on T-complexity

The Titchener T-complexity C_T 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 C_T 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 C_T into a measure with linear upper bound such as Titchener´s T-information. For this reason, the upper bound of C_T has been investigated before by several authors, with various asymptotic solutions proposed. We present a new analytic closed-form asymptotic upper bound for C_T based on the Hurwitz-Lerch zeta function.