Complexity of Reconfiguration in Surface Chemical Reaction Networks

Authors

Robert M. Alaniz, The University of Texas Rio Grande Valley
Josh Brunner
Michael Coulombe
Erik D. Demaine
Yevhenii Diomidov
Ryan Knobel
Timothy Gomez
Elise Grizzell, The University of Texas Rio Grande Valley
Jayson Lynch
Andrew Rodriguez, The University of Texas Rio Grande Valley
Robert Schweller, The University of Texas Rio Grande Valley
Tim Wylie, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

10-2023

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).

Comments

© Robert M. Alaniz, Josh Brunner, Michael Coulombe, Erik D. Demaine, Yevhenii Diomidov, Ryan Knobel, Timothy Gomez, Elise Grizzell, Jayson Lynch, Robert Schweller, and Tim Wylie, UTRGV

Recommended Citation

Alaniz, Robert M., et al. "Complexity of Reconfiguration in Surface Chemical Reaction Networks." arXiv preprint arXiv:2303.15556 (2023).