I haved solved the Parity-4 problem using an artificial neural network called Multilayer Perceptron and populer learning algorithm Backpropagation algorithm. Sigmoid 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.
If the network were not able to converge, start the application again. It will use a different start coordinates for backpropagation algorithm.