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Brief Announcement: Reachability in Deletion-Only Chemical Reaction Networks

Authors Bin Fu, Timothy Gomez, Ryan Knobel, Austin Luchsinger, Aiden Massie, Marco Rodriguez, Adrian Salinas, Robert Schweller, Tim Wylie

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Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Theory of computation → Problems, reductions and completeness
Keywords
  • CRN
  • Chemical Reaction Network
  • Reachability
  • Void Reactions

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Abstract

For general discrete Chemical Reaction Networks (CRNs), the fundamental problem of reachability - the question of whether a target configuration can be produced from a given initial configuration - was recently shown to be Ackermann-complete. However, many open questions remain about which features of the CRN model drive this complexity. We study a restricted class of CRNs with void rules, reactions that only decrease species counts. We further examine this regime in the motivated model of step CRNs, which allow additional species to be introduced in discrete stages. With and without steps, we characterize the complexity of the reachability problem for CRNs with void rules. We show that, without steps, reachability remains polynomial-time solvable for bimolecular systems but becomes NP-complete for larger reactions. Conversely, with just a single step, reachability becomes NP-complete even for bimolecular systems. Beyond what is contained in this brief announcement, we also investigate optimization variants of reachability, provide approximation results for maximizing species deletion, establish ETH-based lower bounds for NP-complete cases, and prove hardness for counting reaction sequences.

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Bin Fu, Timothy Gomez, Ryan Knobel, Austin Luchsinger, Aiden Massie, Marco Rodriguez, Adrian Salinas, Robert Schweller, and Tim Wylie. Brief Announcement: Reachability in Deletion-Only Chemical Reaction Networks. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 23:1-23:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SAND.2025.23

Author Details

Bin Fu
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Timothy Gomez
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Ryan Knobel
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Austin Luchsinger
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Aiden Massie
  • University of Texas Rio Grande Valley, Edinburg, TX, USA
Marco Rodriguez
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Adrian Salinas
  • 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

Funding

This research was supported in part by National Science Foundation Grant CCF-2329918.

References

  1. Robert M. Alaniz, Bin Fu, Timothy Gomez, Elise Grizzell, Andrew Rodriguez, Robert Schweller, and Tim Wylie. Reachability in restricted chemical reaction networks, 2022. URL: https://doi.org/10.48550/arXiv.2211.12603.
  2. Rachel Anderson, Alberto Avila, Bin Fu, Timothy Gomez, Elise Grizzell, Aiden Massie, Gourab Mukhopadhyay, Adrian Salinas, Robert Schweller, Evan Tomai, and Tim Wylie. Computing threshold circuits with void reactions in step chemical reaction networks. In 10th conference on Machines, Computations and Universality (MCU 2024), 2024. Google Scholar
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