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The problem of cognitive access of channels of primary users by a secondary user is considered. The transmissions of primary users are modeled as independent continuous-time Markovian on-off processes. A secondary cognitive user employs a slotted transmission format, and it senses one of the possible channels before transmission. The objective of the cognitive user is to maximize its throughput subject to collision constraints imposed by the primary users. The optimal access strategy is in general a solution of a constrained partially observable Markov decision process, which involves a constrained optimization in an infinite dimensional functional space. It is shown in this paper that, when the collision constraints are tight, the optimal access strategy can be implemented by a simple memoryless access policy with periodic channel sensing. Analytical expressions are given for the thresholds on collision probabilities for which memoryless access performs optimally. Extensions to multiple secondary users are also presented. Numerical and theoretical results are presented to validate and extend the analysis for different practical scenarios.