Boolean Matrices and the Stability of Neural Nets

The functional states of a neural (combinational) net of prescribed interconnection geometry and over-all net function are characterized and enumerated. The problem is formalized for a class of nets having an arbitrary number of inputs and outputs by introducing the notion of a Boolean matrix. The concept of stability of neural nets (which is closely related to the set of functional states over which the input-output function is invariant) is precisely defined and evaluated for certain general classes of nets.