The synthesis of combinational logic to generate probabilities

As CMOS devices are scaled down into the nanometer regime, concerns about reliability are mounting. Instead of viewing nano-scale characteristics as an impediment, technologies such as PCMOS exploit them as a source of randomness. The technology generates random numbers that are used in probabilistic algorithms. With the PCMOS approach, different voltage levels are used to generate different probability values. If many different probability values are required, this approach becomes prohibitively expensive. In this work, we demonstrate a novel technique for synthesizing logic that generates new probabilities from a given set of probabilities. Three different scenarios are considered in terms of whether the given probabilities can be duplicated and whether there is freedom to choose them. In the case that the given probabilities cannot be duplicated and are predetermined, we provide a solution that is FPGA-mappable. In the case that the given probabilities cannot be duplicated but can be freely chosen, we provide an optimal choice. In the case that the given probabilities can be duplicated and can be freely chosen, we demonstrate how to generate arbitrary decimal probabilities from small sets -- a single probability or a pair of probabilities -- through combinational logic.