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Bonding Grammars

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Unconventional Computation and Natural Computation (UCNC 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14776))

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Abstract

We introduce bonding grammars, a graph grammar formalism developed to model DNA computation. It is a modification of fusion grammars introduced by Kreowski, Kuske and Lye in 2017. Bonding is a graph transformation that consists of merging two hyperedges into a single larger one. We show why bonding models DNA pairing better than fusion. Then, we investigate properties of bonding grammars. First, we study the relationship between bonding grammars and hyperedge replacement grammars proving that the classes of languages generated by them are incomparable. Secondly, we prove that bonding grammars naturally generalise regular sticker systems. Finally, we prove that the membership problem for bonding grammars is NP-complete.

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Notes

  1. 1.

    The notation \(\otimes \) refers to the multiplicative conjunction of linear logic. Linear logic is usually considered as a logic of resources, and the formula \(A \otimes B\) of linear logic stands for a combination of a resource of type A and a resource of type B. This interpretation is similar to the one from this work. It is interesting to study whether bonding and other operations on DNA molecules can be described using linear logic.

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Acknowledgments

This work was performed at the Steklov International Mathematical Center and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2022-265).

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  1. Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina Street, Moscow, 119991, Russian Federation

    Tikhon Pshenitsyn

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  1. Tikhon Pshenitsyn
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Correspondence to Tikhon Pshenitsyn .

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  1. Ajou University, Suwon, Korea (Republic of)

    Da-Jung Cho

  2. Pohang University of Science and Technology, Pohang, Korea (Republic of)

    Jongmin Kim

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Pshenitsyn, T. (2024). Bonding Grammars. In: Cho, DJ., Kim, J. (eds) Unconventional Computation and Natural Computation. UCNC 2024. Lecture Notes in Computer Science, vol 14776. Springer, Cham. https://doi.org/10.1007/978-3-031-63742-1_1

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  • DOI: https://doi.org/10.1007/978-3-031-63742-1_1

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