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The problem of dynamically accessing a set of parallel channels occupied by primary users is considered. The secondary user is allowed to sense and to transmit in a single channel. By exploiting idle periods between bursty transmissions of primary users, and by using a periodic sensing strategy, optimal dynamic access is achieved by maximizing the throughput of the secondary user while constraining collision probability with the primary user. The optimal dynamic spectrum access problem can then be formulated within the framework of constrained Markov decision processes (CMDPs). The optimal control policy is identified via a linear program, and its performance is analyzed numerically and through Monte Carlo simulations. Finally, we compare the optimal scheme to an ideal benchmark case when simultaneous sensing of all channels is assumed.