Abstract
Two specific mappings called doubler f d and linearizer \(f_{\ell}\) are introduced to bridge between two kinds of languages. Specifically, f d maps string languages into (double-stranded) molecular languages, while \(f_{\ell}\) performs the opposite mapping. Using these mappings, we obtain new characterizations for the families of sticker languages and of Watson-Crick languages, which lead to not only a unified view of the two families of languages but also provide a helpful view on the computational capability of DNA complementarity. Furthermore, we introduce a special type of a projection f pr which is composed of f d and a projection in the usual sense. We show that any recursively enumerable language L can be expressed as f pr (L m ) for a minimal linear language L m . This result can be strengthened to L = f pr (L s ), for a specific form of minimal linear language L s , which provides a simple morphic characterization for the family of recursively enumerable languages.
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Acknowledgements
Many thanks are due to two anonymous referees for their valuable comments and suggestions that greatly improved an early draft of this paper. This work is supported in part by Grant-in-Aid for Scientific Research on Priority Area no. 14085205, Ministry of Education, Culture, Sports, Science and Technology of Japan and for the Research Institute for Science and Technology of Tokyo Denki University with no.Q07J-05.
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A preliminary version of this article appeared in Onodera and Yokomori (2006).
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Onodera, K., Yokomori, T. Doubler and linearizer: an approach toward a unified theory for molecular computing based on DNA complementarity. Nat Comput 7, 125–143 (2008). https://doi.org/10.1007/s11047-007-9057-5
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DOI: https://doi.org/10.1007/s11047-007-9057-5