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In this paper we propose cognitive medium access (CMA), a protocol aimed at improving coexistence with a set of independently evolving WLAN bands. A time-slotted physical layer for the cognitive radio is considered and CMA is derived based on experimental models. By recasting the problem as a constrained Markov decision process (CMDP), throughput is optimized while keeping interference below some given constraint. The optimal control policy is obtained via linear programming. In addition, we show that optimal CMA admits structured solutions which are computationally less expensive and allow further insight into the problem. Numerical results are presented for typical coexistence setups and show a significant performance improvement.