The ability to efficiently infer the structure of Boolean networks has immense potential for understanding the regulatory interactions in real genetic networks. We have considered a learning strategy that is well suited for situations in which inconsistencies in observations are likely to occur. This strategy produces a Boolean network that makes as few misclassifications as possible and is a generalization of the well-known Consistency Problem. We have focused on the computational complexity of this problem. It turns out that for many function classes, the Best-Fit Extension Problem for Boolean networks is polynomial-time solvable, including those networks having bounded indegree and those in which no assumptions whatsoever about the functions are made. This promising result provides motivation for developing efficient algorithms for inferring network structures from gene expression data.