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The main challenges of cognitive radio include spectrum sensing at the physical (PHY) layer to detect the activity of primary users and spectrum sharing at the medium access control (MAC) layer to coordinate access among coexisting secondary users. In this paper, we consider a cognitive radio network in which a primary user shares a channel with secondary users that cannot distinguish the signals of the primary user from those of a secondary user. We propose a class of distributed cognitive MAC protocols to achieve efficient spectrum sharing among the secondary users while protecting the primary user from potential interference by the secondary users. By using a MAC protocol with one-slot memory, we can obtain high channel utilization by the secondary users while limiting interference to the primary user at a low level. The results of this paper suggest the possibility of utilizing MAC protocol design in cognitive radio networks to overcome limitations in spectrum sensing at the PHY layer as well as to achieve spectrum sharing at the MAC layer.