On a decomposition of Boolean functions represented by quadratic inequalities

This paper advances results on Boolean threshold function decomposition [2] to Boolean functions represented by one quadratic inequalities. Quadratic polynoms are the most compact non-linear polynoms and this property sometimes is quite important. We proved three criterions for non-trivial decomposition of quadratic Boolean threshold function. The second one can be applied without analysis of truth table and only needs some evolvement of threshold structure.
Threshold functions provide a simple but fundamental model for many questions investigated in image recognition, artificial neural networks and many other areas [3].