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  "path": "/abs/2604.17510v1",
  "publishedAt": "2026-04-21T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Divya Bajaj",
    "Bin Fu",
    "Ryan Knobel",
    "Austin Luchsinger",
    "Aiden Massie",
    "Pablo Santos",
    "Ramiro Santos",
    "Robert Schweller",
    "Evan Tomai",
    "Tim Wylie"
  ],
  "textContent": "**Authors:** Divya Bajaj, Bin Fu, Ryan Knobel, Austin Luchsinger, Aiden Massie, Pablo Santos, Ramiro Santos, Robert Schweller, Evan Tomai, Tim Wylie\n\nChemical 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.",
  "title": "Reachability with Restricted Reactions in Inhibitory Chemical Reaction Networks"
}