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In this paper, we exploit the benefits of full-duplex (FD) transmission and reconfigurable intelligent surfaces (RISs) by considering a bidirectional full-duplex wireless communication system with the support of RISs. Specifically, cooperative communications are applied at two FD terminals in a RISs-assisted bidirectional full-duplex (RIS-FD) system. In this context, we successfully derive the mathematical expressions of the outage probability (OP) and the ergodic capacity (EC) of the RIS-FD system with a direct link between two terminals and multiple reflecting paths created by RISs over the Rayleigh fading channel. Numerical results show that the performance of the considered RIS-FD system depends significantly on the total number of reflecting elements in the RISs. Particularly, when the total number of reflecting elements is small, the OP and EC saturate at a high signal-to-noise ratio (SNR). However, when the total number …