Multi-Valued Logic Gates, Continuous Sensitivity, Reversibility, and Threshold Functions

We define an invariant of a multi-valued logic gate by considering the number of certain threshold functions associated with the gate. We call this invariant the continuous sensitivity of the gate. We discuss a method for analysing continuous sensitivity of a multi-valued logic gate by using experimental data about the gate. In particular, we will show that this invariant provides a lower bound for the sensitivity of a boolean function considered as a multi-valued logic gate. We also discuss how continuous sensitivity can be used to understand the reversibility of the Fourier series expansion of a multi-valued logic gate.