Since the completion of the cell lineage of the nematode Caenorhabditis elegans, key genes have been identified in cell fate specification. In particular, the gene pal-1 is required for development of ectoderm and muscle tissue cells during embryogenesis, while other genes have been implicated as regulators of tissue development. Of biological importance is the description of the network of interactions among these tissue identity genes. In this study we utilized the systems-biology approach of reverse engineering, that is, the construction of mathematical models based on system-wide observations, to model the network of the tissue identity genes specified by pal-1. We developed an algorithm using tools from computational algebra to construct polynomial dynamical systems (PDSs) from experimental data. In this setting PDS are generalizations of Boolean networks and have the mathematical structure required to algebraically describe discrete model spaces. The algorithm computes the space of all PDSs that fit a given data set which allows for selection of minimal models via Groebner bases. We applied the algorithm to microarray time series data for a collection of pal-1-dependent genes. Predictions of the reverse-engineered model include two regulatory modules: one for muscle development, which is largely supported by the literature, and one for ectoderm development for which little is currently known.