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Complexity of Reconfiguration in Surface Chemical Reaction Networks

Authors Robert M. Alaniz, Josh Brunner, Michael Coulombe, Erik D. Demaine, Jenny Diomidova, Timothy Gomez, Elise Grizzell, Ryan Knobel, Jayson Lynch, Andrew Rodriguez, Robert Schweller, Tim Wylie

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Robert M. Alaniz
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Josh Brunner
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Michael Coulombe
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Erik D. Demaine
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Jenny Diomidova
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Timothy Gomez
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Elise Grizzell
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Ryan Knobel
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Jayson Lynch
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Andrew Rodriguez
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Robert Schweller
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Tim Wylie
  • University of Texas Rio Grande Valley, Edinburg, TX, USA

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Robert M. Alaniz, Josh Brunner, Michael Coulombe, Erik D. Demaine, Jenny Diomidova, Timothy Gomez, Elise Grizzell, Ryan Knobel, Jayson Lynch, Andrew Rodriguez, Robert Schweller, and Tim Wylie. Complexity of Reconfiguration in Surface Chemical Reaction Networks. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.DNA.29.10

Abstract

We analyze the computational complexity of basic reconfiguration problems for the recently introduced surface Chemical Reaction Networks (sCRNs), where ordered pairs of adjacent species nondeterministically transform into a different ordered pair of species according to a predefined set of allowed transition rules (chemical reactions). In particular, two questions that are fundamental to the simulation of sCRNs are whether a given configuration of molecules can ever transform into another given configuration, and whether a given cell can ever contain a given species, given a set of transition rules. We show that these problems can be solved in polynomial time, are NP-complete, or are PSPACE-complete in a variety of different settings, including when adjacent species just swap instead of arbitrary transformation (swap sCRNs), and when cells can change species a limited number of times (k-burnout). Most problems turn out to be at least NP-hard except with very few distinct species (2 or 3).

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Chemical Reaction Networks
  • reconfiguration
  • hardness

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