A new application of finite automata as computers of real functions is
introduced. It is shown that even automata with a restricted structur
e compute all polynomials, many fractal-like and other functions. Amon
g the results shown, the authors give necessary and sufficient conditi
ons for continuity, show that continuity and equivalence are decidable
properties, and show how to compute integrals of functions in the aut
omata representation.