Synthesis of polynomial functions

Abstract

This chapter addresses the fundamental question: what functions can stochastic logic compute? We show that, given stochastic inputs, any combinational circuit computes a polynomial function. Conversely, we show that, given any polynomial function, we can synthesize stochastic logic to compute this function. The only restriction is that we must have a function that maps the unit interval [0, 1] to the unit interval [0, 1], since the stochastic inputs and outputs are probabilities. Our approach is both general and efficient in terms of area. It can be used to synthesize arbitrary polynomial functions. Through polynomial approximations, it can also be used to synthesize non-polynomial functions.