The gene networks that comprise the circadian clock modulate biological function across a range of scales, from gene expression to performance and adaptive behavior. In recent years, computational models of these networks based on differential equations have become useful tools for quantifying the complex regulatory relationships underlying the clock's oscillatory dynamics. However, optimizing the large parameter sets characteristic of these models places intense demands on both computational and experimental resources, limiting the scope of in silico studies. Here, we present an approach based on Boolean logic that dramatically reduces the parameterization, making the state and parameter spaces finite and tractable. Through the construction of Boolean models fitted to both synthetic and experimental time courses, we show that logic models can reproduce the complex responses to environmental inputs generated by more detailed differential equation formulations. In particular, our work demonstrates that logic models have sufficient predictive power to identify optimal regulatory structures from experimental data. We suggest that the capacity of logic models to provide a computationally efficient representation of system behavior could facilitate the reverse-engineering of large-scale biochemical networks, including circuits characterized by steady state dynamics.