Abstract
Template-guided recombination (TGR) is a formal model for the DNA rearrangement which occurs in certain ciliates. In this paper, the equivalence problem for TGR is considered: given two sets of templates, is their action is the same for all operands? This question is motivated by molecular computation, as we view equivalence in TGR as a method for discerning whether modifications to the functioning of a ciliate via the set of templates has any effect on the rearrangement it defines. This motivation is also suggested by recent experiments into the role of RNA in the rearrangement of ciliate DNA. We give a language-theoretic characterization of equivalence which leads to decidability results for common language classes. In particular, we show a positive answer for regular sets of templates. For context-free sets of templates, the answer is negative. The same language-theoretic characterization also applies to intra-molecular TGR. The problem for iterated TGR remains open.
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Acknowledgments
We thank the referees of DNA 13 for their helpful comments on an early version of this paper, and in particular, the suggested alternative proof of Corollary 8. We also thank the referees of Natural Computing for their many useful and helpful comments.
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Research supported in part by a grant from NSERC. A preliminary version of this paper appeared at DNA 13 [Domaratzki M (2008) Equivalence in template-guided recombination. In: Garzon M, Yan H (eds) DNA 13. Springer, LNCS 4848, pp 263–272].
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Domaratzki, M. Equivalence in template-guided recombination. Nat Comput 7, 439–449 (2008). https://doi.org/10.1007/s11047-008-9071-2
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DOI: https://doi.org/10.1007/s11047-008-9071-2