Optimizing multi-level combinational circuits for generating random bits

Random bits are an important construct in many applications, such as hardware-based implementation of probabilistic algorithms and weighted random testing. One approach in generating random bits with required probabilities is to synthesize combinational circuits that transform a set of source probabilities into target probabilities. In [1], the authors proposed a greedy algorithm that synthesizes circuits in the form of a gate chain to approximate target probabilities. However, since this approach only considers circuits of such a special form, the resulting circuits are not satisfactory both in terms of the approximation error and the circuit depth. In this paper, we propose a new algorithm to synthesize combinational circuits for generating random bits. Compared to the previous one, our approach greatly enlarges the search space. Also, we apply a linear property of probabilistic logic computation and an iterative local search method to increase the efficiency of our algorithm. Experimental results comparing the approximation errors and the depths of the circuits synthesized by our method to those of the circuits synthesized by the previous approach demonstrate the superiority of our method.