I haved solved the Parity-3 problem using an artificial neural network called Multilayer Perceptron and populer learning algorithm Backpropagation algorithm. Hyperbolic tangent has been used as an activation(transfer) function .
You must start the app with ParityNStart.m file in MATLAB. If MATLAB have a hard time to start parityNStart, you may have to shorten this dictionary name. It only should include English characters without any blanks. Best Regards.