Theses and Dissertations

Date of Award

12-1-2025

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Computer Science

First Advisor

Timothy Wylie

Second Advisor

Bin Fu

Third Advisor

Robert Schweller

Abstract

Chemical Reaction Networks (CRNs) are a system of abstraction of real-world chemical dynamics. Each CRN system is defined as a pair of molecular species and reaction rules, which consume a set of reactant species and create a new set of product species. In this paper, we investigate the simple class of void reactions, which cannot create new species and are computationally weak with small-enough sizes in basic CRNs. Here, we study their computational expression in more powerful extended CRN models. Specifically, we consider the Step CRN model, in which new species are added into the system through a sequence of steps, and the Inhibitory CRN model, in which reactions can be blocked from running if specific species are present in the system. We also look at a slight modification to the Step CRN model in which the system continuously repeats through its step-sequence, which we term the Step-Cycle CRN model.

We first show that Step CRNs can compute Threshold Circuits even when only using trimolecular or bimolecular void reactions. We then look at the CRN reachability problem, which asks if a configuration of species can transform in another configuration. Although reachability with only bimolecular void reactions is polynomial-time solvable in basic CRNs, we prove that reachability under the same restrictions becomes NP-complete in the Step and Inhibitory CRN models. Finally, we show that the Step-Cycle CRN model, even when restricted to only using void reactions of size at most (3,1), can simulate any given basic, Step, or Step-Cycle CRN under polynomial resources; thus, the Step-Cycle model remains Turing universal under this restriction.

Comments

Copyright 2025 Aiden J. Massie. All Rights Reserved. https://proquest.com/docview/3292599857

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