Fractal encoding of context-free grammars in connectionist networks

Connectionist network learning of context free languages has so far been applied only to very simple cases and has often made use of an external stack. Learning complex context free languages with a homogeneous neural mechanism looks like a much harder problem. The current paper takes a step toward solving this problem by analyzing context free grammar computation (without addressing learning) in a class of analog computers called Dynamical Automata, which are naturally implemented in connectionist networks. The result is a widely applicable method of using fractal sets to organize infinite state computations in a bounded state space. An appealing consquence is the development of parameter-space maps, which locate various complex computers in spatial relationships to one another. An example suggests that such a global perspective on the organization of the parameter space may be helpful for solving the hard problem of getting connectionist networks to learn complex grammars from examples.