# American Institute of Mathematical Sciences

May  2020, 14(2): 307-318. doi: 10.3934/amc.2020022

## Algebraic dependence in generating functions and expansion complexity

 1 Department of Mathematics, University of Cantabria, Santander 39005, Spain 2 Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Straße 69, A-4040 Linz, Austria

* Corresponding author: László Mérai

Received  July 2018 Revised  April 2019 Published  September 2019

In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. Recently, a series of paper has been published for analysis of expansion complexity and for testing sequences in terms of this new measure of randomness. In this paper, we continue this analysis. First we study the expansion complexity in terms of the Gröbner basis of the underlying polynomial ideal. Next, we prove bounds on the expansion complexity for random sequences. Finally, we study the expansion complexity of sequences defined by differential equations, including the inversive generator.

Citation: Domingo Gómez-Pérez, László Mérai. Algebraic dependence in generating functions and expansion complexity. Advances in Mathematics of Communications, 2020, 14 (2) : 307-318. doi: 10.3934/amc.2020022
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