On the Computation of Boolean Functions by Analog Circuits of Bounded Fan-in (Extended Abstract)

W e consider the complexity of computing Boolean functions b y analog circuits of bounded fan-in, i.e. b y circuits of gates computing real-valued functions, either exactly or as a sign-representation. Sharp upper bounds are obtained for the complexity of the most &@cult n-variable function over certain bases (signrepresentation by arithmetic circuits and exact computation b y piecewise linear circuits). Bounds are given for the computational power gained by adding discontinuous gate functions and nondeterminism. W e also prove explicit nonlinear lower bounds for the formula size of analog circuits over bases containing addition, subtraction, multiplication, the sign function and all real constants.