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Bioinformatics is an active research area aimed at developing intelligent systems for analyses of molecular biology. Many methods based on formal language theory, statistical theory, and learning theory have been developed for modeling and analyzing biological sequences such as DNA, RNA, and proteins. Especially, grammatical inference methods are expected to find some grammatical structures hidden in biological sequences. In this article, we give an overview of a series of our grammatical approaches to biological sequence analyses and related researches and focus on learning stochastic grammars from biological sequences and predicting their functions based on learned stochastic grammars.