Boolean networks are a popular model class for capturing the interactions of genes and global dynamical behavior of genetic regulatory networks. Recently, a significant amount of attention has been focused on the inference or identification of the model structure from gene expression data. We consider the Consistency as well as Best-Fit Extension problems in the context of inferring the networks from data. The latter approach is especially useful in situations when gene expression measurements are noisy and may lead to inconsistent observations. We propose simple efficient algorithms that can be used to answer the Consistency Problem and find one or all consistent Boolean networks relative to the given examples. The same method is extended to learning gene regulatory networks under the Best-Fit Extension paradigm. We also introduce a simple and fast way of finding all Boolean networks having limited error size in the Best-Fit Extension Problem setting. We apply the inference methods to a real gene expression data set and present the results for a selected set of genes.
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