Functional decomposability criteria for quadratic threshold Boolean functions

Threshold functions provide a simple but fundamental model for many questions investigated in image recognition, artificial neural networks and many other areas. In this paper, the results in Boolean threshold function decomposition are advanced to Boolean functions represented by one quadratic inequality. Quadratic polynomials are the most compact non-linear polynomials and this property sometimes is quite important. We prove three criteria for non-trivial decomposition of quadratic Boolean threshold functions. One of them can be applied without analysis of truth table and only uses the threshold structure parameters.