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Using DNA to store digital signals, or data in general, offers significant advantages when compared to other media. The DNA molecule, especially in its double-stranded form, is very stable, compact, and inexpensive. In the past, we have shown that DNA can be used to store and retrieve digital signals encoded and stored in DNA. We have also shown that DNA hybridization can be used as a similarity criterion for retrieving digital signals encoded and stored in a DNA database. Retrieval is achieved through hybridization of ??query?? and ??data?? DNA molecules. In this paper, we present a mathematical framework to simulate single-query and parallel-query scenarios, and to estimate hybridization efficiency. Our framework allows for exact numerical solutions as well as closed-form approximations under certain conditions. Similarly to the digital domain, we define a DNA SNR measure to assess the performance of the DNA-based retrieval scheme in terms of database size and source statistics. With approximations, we show that the SNR of any finite-sized DNA-based database is upper bounded by the SNR of an infinitely large DNA-based database that has the same source distribution. Computer simulations are presented to validate our results.