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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 (ER) 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 …