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Neural networks are considered as promising candidates for implementing functions in memristor crossbar array with high tolerance to device defects and variations. Based on such arrays, Neural Logic Blocks (NLB) with learning capability can be built to replace Configurable Logic Block (CLB) in programmable logic circuits. In this article, we describe a neural learning method to implement Boolean functions in memristor NLB. By using Monte-Carlo simulation, we demonstrate its high robustness against most important device defects and variations, like static defects and memristor voltage threshold variability.