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Reachability with Restricted Reactions in Inhibitory Chemical Reaction Networks

Authors Divya Bajaj, Bin Fu, Ryan Knobel, Austin Luchsinger, Aiden Massie, Pablo Santos, Ramiro Santos, Robert Schweller, Evan Tomai, Tim Wylie

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LIPIcs.SWAT.2026.3.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Theory of computation → Complexity classes
Keywords
  • Chemical Reaction Networks
  • Vector Addition Systems
  • Petri-nets
  • Reachability
  • Inhibitors
  • Void Reactions

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Abstract

Chemical Reaction Networks (CRNs) are a well-established model of distributed computing characterized by quantities of molecular species that can transform or change through applications of reactions. A fundamental problem in CRNs is the reachability problem, which asks if an initial configuration of species can transition to a target configuration through an applicable sequence of reactions. It is well-known that the reachability problem in general CRNs was recently proven to be Ackermann-complete. However, if the CRN’s reactions are restricted in both power, such as only deleting species (deletion-only rules) or consuming and producing an equal number of species (volume-preserving rules), and size (unimolecular or bimolecular rules), then reachability falls below Ackermann-completeness, and is even solvable in polynomial time for deletion-only systems.
In this paper, we investigate reachability under this set of restricted unimolecular and bimolecular reactions, but in the Priority-Inhibitory CRN and Inhibitory CRN models. These models extend a traditional CRN by allowing some reactions to be inhibited from firing in a configuration if certain species are present; the exact inhibition behavior varies between the models. We first show that reachability with Priority iCRNs mostly remains in P for deletion-only systems, but becomes NP-complete for one case. We then show that reachability with deletion-only reactions for iCRNs is mostly NP-complete, and PSPACE-complete even for (1,1)-size (general) reactions. We also provide FPT algorithms for solving most of the reachability problems for the iCRN model. Finally, we show reachability for CRNs with states is already NP-hard for the simplest deletion-only systems, and is PSPACE-complete even for (general) (1,1)-size reactions.

Cite As Get BibTex

Divya Bajaj, Bin Fu, Ryan Knobel, Austin Luchsinger, Aiden Massie, Pablo Santos, Ramiro Santos, Robert Schweller, Evan Tomai, and Tim Wylie. Reachability with Restricted Reactions in Inhibitory Chemical Reaction Networks. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SWAT.2026.3

Author Details

Divya Bajaj
  • University of Texas Rio Grande Valley, TX, USA
Bin Fu
  • University of Texas Rio Grande Valley, TX, USA
Ryan Knobel
  • University of Texas Rio Grande Valley, TX, USA
Austin Luchsinger
  • University of Texas Rio Grande Valley, TX, USA
Aiden Massie
  • University of Texas Rio Grande Valley, TX, USA
Pablo Santos
  • University of Texas Rio Grande Valley, TX, USA
Ramiro Santos
  • University of Texas Rio Grande Valley, TX, USA
Robert Schweller
  • University of Texas Rio Grande Valley, TX, USA
Evan Tomai
  • University of Texas Rio Grande Valley, TX, USA
Tim Wylie
  • University of Texas Rio Grande Valley, TX, USA

Funding

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

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