Reachability with Restricted Reactions in Inhibitory Chemical Reaction Networks

2026-04-19

AI Summary

This study investigates the configuration reachability problem in chemical reaction networks (CRNs) equipped with inhibition mechanisms under restricted reaction types—specifically unimolecular, bimolecular, and deletion-only reactions. By leveraging computational complexity theory and formal modeling, it provides the first systematic characterization of the complexity boundaries for reachability under both priority-based and general inhibition models. The work reveals a sharp transition in complexity ranging from P to PSPACE-complete: for instance, deletion-only systems are mostly in P under priority inhibition but become NP-complete under general inhibition, while reachability for (1,1)-size reactions is shown to be PSPACE-complete. Furthermore, the paper develops several fixed-parameter tractable (FPT) algorithms for key cases, offering efficient solutions within specific parameterized settings.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

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.

Problem

• reachability
• inhibitory chemical reaction networks
• restricted reactions
• computational complexity
• deletion-only systems

Innovation

• Inhibitory Chemical Reaction Networks
• Reachability Problem
• Computational Complexity
• Fixed-Parameter Tractability
• Deletion-only Reactions