  This paper is motivated by the theory of sequential dynamical systems,
developed as a basis for a mathematical theory of computer simulation. It
contains a classification of finite dynamical systems on binary strings, which
are obtained by composing functions defined on the coordinates. The
classification is in terms of the dependency relations among the coordinate
functions. It suggests a natural notion of the linearization of a system.
Furthermore, it contains a sharp upper bound on the number of systems in terms
of the dependencies among the coordinate functions. This upper bound
generalizes an upper bound for sequential dynamical systems.
