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Extracting reaction systems from function behavior

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Abstract

Reaction systems, introduced by Ehrenfeucht and Rozenberg, are a theoretical model of computation based on the two main features of biochemical reactions: facilitation and inhibition, which are captured by the individual reactions of the system. All reactions, acting together, determine the global behavior or the result function, res, of the system. In this paper, we study decomposing of a given result function to find a functionally equivalent set of reactions. We propose several approaches, based on identifying reaction systems with Boolean functions, Boolean formulas, and logic circuits. We show how to minimize the number of reactions and their resources for each single output individually, as a group, and when only a subset of the states are considered. These approaches work both when the reactions of the given res function are known and not known. We characterize the minimal number of reactions through the minimal number of logical terms of the Boolean formula representation of the reaction system. Finally, we make applications recommendations for our findings.

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Notes

  1. Logic Friday 1.1.4, (c) Steve Rickman.

  2. Although the cells of the Karnaugh map themselves are ordered according to a Gray code, it is still a surprise to see the code clearly spelled out in the diagram.

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Acknowledgements

This research was initiated at and facilitated by the 2nd International Workshop in Reaction Systems and 1st School in Reaction Systems held on June 3, 2019, organized by Nicolaus Copernicus University, Toruń, Poland. DG and HJH acknowledge travel support from InterAPS (International Academic Partnerships in Sciences with Nicolaus Copernicus University) and from the University of North Florida, USA. The authors thank Matthew Thomas for useful comments on a previous version of this paper. The authors are also very grateful for the thoughtful suggestions from three anonymous referees, which have improved the presentation of this paper.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of North Florida, 32224, Jacksonville, FL, USA

    Daniela Genova

  2. LIACS, Leiden University, Leiden , The Netherlands

    Hendrik Jan Hoogeboom

  3. School of Computing, University of North Florida, Jacksonville, FL, 32224, USA

    Zornitza Prodanoff

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  1. Daniela Genova
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  2. Hendrik Jan Hoogeboom
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  3. Zornitza Prodanoff
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Correspondence to Daniela Genova.

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Genova, D., Hoogeboom, H.J. & Prodanoff, Z. Extracting reaction systems from function behavior. J Membr Comput 2, 194–206 (2020). https://doi.org/10.1007/s41965-020-00045-z

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