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In this paper we design a cognitive radio that can coexist with multiple parallel WLAN channels while abiding by an interference constraint. The interaction between both systems is characterized by measurement and coexistence is enhanced by predicting the WLAN's behavior based on a continuous-time Markov chain model. Cognitive medium access (CMA) is derived from this model by recasting the problem as one of constrained Markov decision processes. Solutions are obtained by linear programming. Furthermore, we show that optimal CMA admits structured solutions, simplifying practical implementations. Preliminary results for the partially observable case are presented. The performance of the proposed schemes is evaluated for a typical WLAN coexistence setup and shows a significant performance improvement.