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Theory of reaction automata: a survey

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Abstract

In this paper, we survey on reaction automata theory to model and analyze the biochemical behaviors of vital reactions occurring in nature. Inspired by two notions of a reaction system initiated by Ehrenfeucht and Rozenberg in 2007 and of a multiset, reaction automata (RAs) have been proposed as computing models for accepting string languages. Given an input sequence of symbols, an RA performs its computation process as follows: at every time of receiving an input symbol, it changes the current configuration (represented by a multiset) by applying reaction rules to the multiset in a prescribed manner, for which two kinds of application manners are considered: the maximally parallel manner and the (usual) sequential manner. An RA functions as an extended finite automaton in which multisets play a role of (unbounded number of) states and the state transition is performed by applying reaction rules. We show that the computational powers of RAs are Turing universal in both manners of rule applications. The relationship between the space-bounded variants of RA and the Chomsky hierarchy is also discussed. Further, we discuss the notion of chemical reaction automata, which is a simplified variant of RAs with reaction rules that are free from inhibitor functioning. We complete this survey with a variety of related models of computing together with future research topics.

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Notes

  1. (In the usual sense in space complexity theory).

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Acknowledgements

The work of T. Yokomori was in part supported by JSPS KAKENHI, Grant-in-Aid for Scientific Research (C) JP17K00021. The work of F. Okubo was in part supported by Grants-in-Aid for Young Scientists (B) No. 24700304, Japan Society for the Promotion of Science.

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  1. Faculty of Education and Integrated Arts and Sciences, Waseda University, 1-6-1 Nishiwaseda, Shinjuku-ku, Tokyo, 169-8050, Japan

    Takashi Yokomori

  2. Nihon Pharmaceutical University, 10281, Komuro, lna-machi, Kitaadachi-gun, Saitama, 362-0806, Japan

    Fumiya Okubo

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  1. Takashi Yokomori
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Yokomori, T., Okubo, F. Theory of reaction automata: a survey. J Membr Comput 3, 63–85 (2021). https://doi.org/10.1007/s41965-021-00070-6

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