  Multivariate polynomial dynamical systems over finite fields have been
studied in several contexts, including engineering and mathematical biology. An
important problem is to construct models of such systems from a partial
specification of dynamic properties, e.g., from a collection of state
transition measurements. Here, we consider static models, which are directed
graphs that represent the causal relationships between system variables,
so-called wiring diagrams. This paper contains an algorithm which computes all
possible minimal wiring diagrams for a given set of state transition
measurements. The paper also contains several statistical measures for model
selection. The algorithm uses primary decomposition of monomial ideals as the
principal tool. An application to the reverse-engineering of a gene regulatory
network is included. The algorithm and the statistical measures are implemented
in Macaulay2 and are available from the authors.
