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Hairpin completions and reductions: semilinearity properties

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Abstract

This paper is part of the investigation of some operations on words and languages with motivations coming from DNA biochemistry, namely three variants of hairpin completion and three variants of hairpin reduction. Since not all the hairpin completions or reductions of semilinear languages remain semilinear, we study sufficient conditions for semilinear languages to preserve their semilinearity property after applying the non-iterated hairpin completion or hairpin reduction. A similar approach is then applied to the iterated variants of these operations. Along these lines, we define the hairpin reduction root of a language and show that the hairpin reduction root of a semilinear language is not necessarily semilinear except the universal language. A few open problems are finally discussed.

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Funding

This work was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, Project Number POC P-37-257. Victor Mitrana has also been supported by the Alexander von Humboldt Foundation.

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Correspondence to Victor Mitrana.

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Bordihn, H., Mitrana, V., Păun, A. et al. Hairpin completions and reductions: semilinearity properties. Nat Comput 20, 193–203 (2021). https://doi.org/10.1007/s11047-020-09797-0

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