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The bionic features offered by memory device are being actively explored. However, two-terminal memristors exhibit variability and limited capacity due to their inherent single presynaptic input scheme. Compared with the two-terminal memristor, the memtransistor can realize the modulation of conductive channel through the synergistic effect of gate, which enables the multifunctional modulation. Here, based on Schottky barrier tuning at metal-semiconductor interfaces by means of ferroelectric domain switching, a programmable memtransistor with arithmetic calculating and logic function is realized. Memtransistor with drain and gate adjustable non-volatile memory function effectively simulates the plasticity of biological synapses. Moreover, four arithmetical operations: addition, subtraction, multiplication and division are carried out by using the synaptic device. At the same time, the logic gate functions of "XOR" and "XNOR" were implemented based on ferroelectric memtransistor. This result will be helpful to further promote the development of memory computing for synaptic devices. [ABSTRACT FROM AUTHOR]