A Novel Heuristic Search Method for Two-level Approximate Logic Synthesis

Recently, much attention has been paid to approximate computing, a novel design paradigm for error-tolerant applications. It can significantly reduce area, power, and delay of circuits by introducing an acceptable amount of error. In this paper, we propose a new heuristic method for two-level approximate logic synthesis. The problem is to identify an approximate sum-of-product (SOP) expression under a given error rate constraint so that it has the fewest literals. The basic idea of our method is to find an optimal set of input combinations for 0-to-1 output complement (SICC). For this purpose, we first identify all prime SICCs, which are fundamental SICCs in the sense that the optimal SICC is very likely to be a union of a subset of the prime SICCs. Then, we search among all subsets of the prime SICCs the optimal subset, which leads to a final good approximate SOP. We further propose four speed-up techniques. The experiments on benchmarks showed that our method is better than the previous state-of-the-art method and our speed-up techniques are effective. For an error rate threshold of 0.8%, our method can reduce 15.8% literals on average.