Optimization Of The Number Of Inverters Based On XOR-majority Graph(XMG)

With the rapid development of the Internet and electronic communications,we are going to embrace the 5G technology in the near future,leading a profound revolution in many related industries(such as artificial intelligence,auto-driving,etc.).Given the high demand of computing speed,it is a must for corporates and researchers to improve performance of integrated circuit in calculate ability,power consuming and time delay.The optimization of the number of inverters is one of the hotspots of optimization today,mainly because the implementation cost of the inverter is relatively high.Currently,the research of optimization focus on the number of inverters,since they are costly in QCA and might cause negative effects for carry-chains of FPGA,such as delay incremental and area enlargement.Plenty of literatures have proposed many optimization methods for inverters in And-Inverter Graph(AIG),Majority-inverter Graph(MIG),etc.,but in order to better support arithmetic operations and get more compact logical graphical expressions,researchers have introduced XOR operations in the MIG,and have proposed heterogeneous logic representation named XOR-Majority Graph(XMG).Nowadays,XMG has been applied widely in quantum circuit synthesis and exact synthesis,which has greatly promoted the development of integrated circuit.The main content of this paper includes the following three parts:1.Optimize the number of inverters without changing the structure and function of the XMG.First understand the structure and distribution of node in the XMG,and use the transmission rules of the inverters on the input and output connections of each node to optimize the number of inverters in the XMG circuit by One-Level Optimization.On the basis of One-Level Optimization,another optimization code program implementation named Two-Level Optimization is added to achieve better optimization results.Finally,based on the previous optimization method,the special transmission of inverters on XOR nodes is considered to form a complete inverter optimization program and then the purpose of reducing circuit implementation costs is achieved.2.Multi-objective optimization of the number of inverters and the number of nodes in the process of graph change.First traverse a special combined structure in the XMG,and then use the potential optimization opportunities during their structure rewriting to optimize the number of nodes;Then optimize the number of inverters after the structure rewriting in the XMG,which realizes the optimization of the number of inverters and the number of nodes at the same time,and finally achieves the purpose of optimizing the circuit area and delay.3.Inversion optimization and circuit design in QCA circuits.Without changing the circuit structure,the inverter optimization method is applied to the QCA circuit to realize the transformation from the theoretical method level to the physical level application.By constructing and designing a cell diagram of the QCA circuit and performing simulation,we get a series of experimental result.Then we compare and analyze the parameters of the energy,area,and cell number of the circuit before and after optimization to further verify the correctness and effectiveness of the optimization method.