Why can't the XOR linear inseparability problem be solved with one perceptron - like this?
Your function


  0,otherwise 1


is not a linear combination of the inputs.

From the definition of single layer perceptronL


  A single layer perceptron (SLP) is a feed-forward network based on a threshold transfer function


Your function has two thresholds:  one for &lt; 1 another for >1