Learning the grammar of a chaotic dynamical system in a format suitable for controlling symbol dynamics and communications

The unique possibility of encoding information into symbol dynamics corresponding to a chaotic transmitter has been demonstrated by Hayes and Grebogi (1993, 1994) and the authors (1997). To take advantage of sensitive dependence by using only small deliberate parameter perturbations requires that we respect the grammar of the symbol dynamics which represents the physical dynamical system. We present a new algorithm to learn the observed grammar of a symbol dynamics in terms of observed transitions between bins defined by the symbol generating partition.