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On the overlap assembly of strings and languages

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Abstract

This paper investigates properties of the binary string and language operation overlap assembly which was defined by Csuhaj-Varjú, Petre and Vaszil as a formal model of the linear self-assembly of DNA strands: The overlap assembly of two strings, xy and yz, which share an “overlap” y, results in the string xyz. The study of overlap assembly as a formal language operation is part of ongoing efforts to provide a formal framework and rigorous treatment of DNA-based information and DNA-based computation. Other studies along these lines include theoretical explorations of splicing systems, insertion/deletion systems, substitution, hairpin extension, hairpin reduction, superposition, overlapping catenation, conditional concatenation, contextual intra- and intermolecular recombinations, template guided recombination, as well as directed extension by PCR. In this context, we investigate overlap assembly and its properties: closure properties of basic language families under this operation, decision problems, as well as the possible use of iterated overlap assembly to generate combinatorial DNA libraries.

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Acknowledgments

This research was supported by a Natural Science and Engineering Council of Canada (NSERC) Discovery Grant R2824A01 and a University of Western Ontario Grant to L.K., and US NSF Grant CCF-1117708 to O.H.I. The authors thank Giuditta Franco for useful suggestions and discussions on experimental aspects of XPCR, as well as Sepinoud Azimi and Florin Manea for pointing out important references.

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Authors and Affiliations

  1. Department of Computer Science, The University of Western Ontario, London, ON, N6A 5B7, Canada

    Srujan Kumar Enaganti, Lila Kari & Steffen Kopecki

  2. Department of Computer Science, University of California Santa Barbara, Santa Barbara, CA, 93106, USA

    Oscar H. Ibarra

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  1. Srujan Kumar Enaganti
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  2. Oscar H. Ibarra
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  3. Lila Kari
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  4. Steffen Kopecki
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Correspondence to Srujan Kumar Enaganti.

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Enaganti, S.K., Ibarra, O.H., Kari, L. et al. On the overlap assembly of strings and languages. Nat Comput 16, 175–185 (2017). https://doi.org/10.1007/s11047-015-9538-x

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