Recurrent neural networks and Fibonacci numeration system of order s(s/spl ges/2)

Abstract

In the Fibonacci numeration system of order s(s/spl ges/2), every positive integer admits a unique representation which does not contain s consecutive digits equal to 1 (called normal form). We show how this normal form can be obtained from any representation by recurrent neural networks. The addition of two integers in this system and the conversion from a Fibonacci representation to a standard binary representation (and conversely) can also be realized using recurrent neural networks.<>