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The smooth scaling of technology over past decades is returning diminished profits as researchers are trying to cope with several challenges posed by CMOS devices. As a result, quest for novel physical media for storage and computing is currently an important research pursuit. Recently a new kind of passive electrical device called memristor is proposed, which can retain its state via the resistance in a non-volatile fashion. It is also experimentally demonstrated to perform material implication, a fundamental logical operation. The capability of a memristive device to do logical operations as well as to retain its state makes it a promising candidate for future technologies. In this paper, we investigate the approximate implementation cost of a multi-level combinational logic while using memristive switches as the target technology. Traditional synthesis algorithms are extended and new heuristics are suggested to reduce the costs significantly.