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arXiv · 2303.15556

Complexity of Reconfiguration in Surface Chemical Reaction Networks

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

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Robert M. Alaniz, Josh Brunner, Michael Coulombe, Erik D. Demaine, Jenny Diomidova, Ryan Knobel, Timothy Gomez, Elise Grizzell, Jayson Lynch, Andrew Rodriguez, Robert Schweller, Tim Wylie. 2023-03-27. Complexity of Reconfiguration in Surface Chemical Reaction Networks. https://arxiv.org/abs/2303.15556

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