The Memristor crossbar array structure provides a low-cost and highly efficient platform for the artificial neural network (ANN) implementation. On the other hand, the implementation of combinational logic circuits using memristor-based platforms has attracted great attention recently. However, the basic operations of a memristor are multiplication (Ohm’s law) and addition (Kirchhoff's circuit laws), which make the implementation of logical operations very complex. To overcome this problem, we propose an ANN-based synthesizer that first translates the combinational logic circuit behavior to a neural network, which would be implemented using a memristor crossbar array. The proposed synthesizer includes a feature extractor and a multilayer perceptron (MLP) to classify the input vectors into 0 or 1 groups. The results show that the delay of an ANN-crossbar circuit is considerably lower than that of the circuit implemented by memristor-based logic gates. Although the accuracy of an ANN-crossbar circuit is not 100% because of the natural behavior of ANN-based applications, an ANN-crossbar circuit could be useful regarding error-resilient systems such as image processing applications. Furthermore, these circuits are appropriate for advanced neuromorphic computers that rely on non-deterministic operations.