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It is still an open problem to identify functional relations with o(N · nk) time for any domain, where N is the number of learning instances, n is the number of genes (or variables) in the gene regulatory network (GRN) models and k is the indegree of the genes. To solve the problem, we introduce a novel algorithm, DFL (discrete function learning), for reconstructing qualitative models of GRNs from gene expression data in this paper. We analyze the complexity of O(k · N · n2) on the average and its data requirements. We also perform experiments on both synthetic and Cho et al. yeast cell cycle gene expression data to validate the efficiency and prediction performance of the DFL algorithm. The experiments of synthetic Boolean networks show that the DFL algorithm is more efficient than current algorithms without loss of prediction performances. The results of yeast cell cycle gene expression data show that the DFL algorithm can identify biologically significant models with reasonable accuracy, sensitivity and high precision with respect to the literature evidences. We further introduce a method called ε function to deal with noises in data sets. The experimental results show that the ε function method is a good supplement to the DFL algorithm.