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This paper introduces an algorithm for the lossless compression of DNA files which contain annotation text besides the nucleotide sequence. First, a grammar is specifically designed to capture the regularities of the annotation text. A revertible transformation uses the grammar rules in order to equivalently represent the original file as a collection of parsed segments and a sequence of decisions made by the grammar parser. This decomposition enables the efficient use of state-of-the-art encoders for processing the parsed segments. The output size of the decision-making process of the grammar is optimized by extending the states to account for high-order Markovian dependencies. The practical implementation of the algorithm achieves a significant improvement when compared to the general-purpose methods currently used for DNA files.