New technologies such as Quantum-dot Cellular Automata (QCA), Single Electron Tunneling (SET), Tunneling Phase Logic (TPL) and all-spin logic (ASL) devices have been widely advocated in nanotechnology as a response to the physical limits associated with complementary metal oxide semiconductor (CMOS) technology in atomic scales. Some of their peculiar features are their smaller size, higher speed, higher switching frequency, lower power consumption, and higher scale integration. In these

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... gies, the majority (or minority) and inverter gates are employed for the production of the functions as this set of gates makes a universal set of Boolean primitives in these technologies. An important step in the generation of Boolean functions using the majority gate is reducing the number of involved gates. In this paper, a multi-objective synthesis methodology (with the objective priority of gate counts, gate levels and the number of inverter gates) is presented for finding the minimal number of possible majority gates in the synthesis of Boolean functions using the proposed Majority Specification Matrix (MSM) concept. Moreover, based on MSM, a synthesis flow is proposed for the synthesis of multi-output Boolean functions. To reveal the efficiency of the proposed method, it is compared with a meta-heuristic method, multi-objective Genetic Programing (GP). Besides, it is applied to synthesize MCNC benchmark circuits. The results are indicative of the outperformance of the proposed method in comparison to multi-objective GP method. Also, for the MCNC benchmark circuits, there is an average reduction of 10.5% in the number of levels as well as 16.8% and 33.5% in the number of majority and inverter gates, as compared to the best available method respectively.