Chebyshev Approximation and Threshold Functions

Where previous authors have considered linear approximations with a minimum sum of squared differences, we consider, instead, Chehyshev linear approximations, which minimize the maximum deviation. We obtain thus: 1) A new characterization of threshold functions, 2) A characterization of optimal threshold realizations as being virtually identical to the Chebyshev-best linear approximations, and 3) A new insight into the test-synthesis problem with which we opened this note.