  We characterize the capacity region of a two-user multiple access channel
(MAC) in a reconfigurable intelligent surface (RIS)-aided communication system
with side information (SI) at the transmitters. We consider two uplink
communication scenarios: (i) a double dirty MAC where the interferences are
known non-causally to both users; and (ii) a single dirty MAC model where only
one of the users knows the interference and the other one is not aware of the
interference. Considering that each of the users is assisted by a different RIS
with Mi elements, we derive closed-form expressions for the capacity region and
the outage probability (OP) for both system models. Results show that the use
of RISs is beneficial to extend the capacity region and improve the OP in both
scenarios.
