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In this paper, a novel concept called simultaneously transmitting and reflecting RIS (STAR-RIS) is introduced into the wireless-powered mobile edge computing (MEC) systems to improve the efficiency of energy transfer and task offloading. Compared with traditional reflecting-only RIS, STAR-RIS extends the half-space coverage to full-space coverage by simultaneously transmitting and reflecting incident signals, and also provides new degrees-of-freedom (DoFs) for manipulating signal propagation. We aim to maximize the total computation rate of all users, where the energy transfer time, transmit power and CPU frequencies of users, and the configuration design of STAR-RIS are jointly optimized. Considering the characteristics of STAR-RIS, three operating protocols, namely energy splitting (ES), mode switching (MS), and time splitting (TS) are studied, respectively. For the ES protocol, based on the penalty …