The classic theory of computation initiated by Turing and his contemporaries provides a theory
of effective procedures  algorithms that can be executed by the human mind, deploying cognitive
processes constituting the conscious rule interpreter. The cognitive processes constituting the human
intuitive processor potentially call for a different theory of computation. Assuming that important
functions computed by the intuitive processor can be described abstractly as symbolic recursive
functions and symbolic grammars, we ask which symbolic functions can be computed by the human
intuitive processor, and how those functions are best specified  given that these functions must
be computed using neural computation. Characterizing the automata of neural computation, we begin
the construction of a class of recursive symbolic functions computable by these automata, and the
construction of a class of neural networks that embody the grammars defining formal languages.
