Recurrent neural networks and Fibonacci numeration system

It is known from Zeckendorf's theorem (1972) that every positive integer admits a representation as a sum of distinct Fibonacci numbers. Furthermore, this representation is unique if it does not contain two consecutive digits that equal to 1 and has no zero to its left hand side. This unique representation is called normal form. Recurrent neural networks have shown to have powerful capabilities for modeling many computational structures. In the present paper we show how to compute normalization and addition in Fibonacci numeration system using recurrent neural networks.