Polynomial Simulations of CRN Models with Trimolecular Void Step-Cycle CRNs

Authors

• Austin Luchsinger, The University of Texas Rio Grande ValleyFollow
• Aiden J. Massie, The University of Texas Rio Grande Valley
• Robert Schweller, The University of Texas Rio Grande ValleyFollow
• Evan Tomai, University of Texas at Dallas
• Tim Wylie, The University of Texas Rio Grande ValleyFollow

Document Type

Conference Proceeding

Publication Date

1-31-2026

Abstract

We investigate the computational power of Step-Cycle Chemical Reaction Networks (CRNs) when restricted to void reactions of size at most (3, 1). Step-Cycle CRNs extend the previously introduced step CRN model by repeatedly cycling through a fixed sequence of species additions and reaction phases. We show that even under the severe constraint of trimolecular void rules—which can only delete or preserve species—the model retains full computational power. In particular, we prove that (3,1) void Step-Cycle CRNs can polynomially simulate (1) any general CRN, (2) any general Step CRN, and (3) any general Step-Cycle CRN. Ultimately, these results demonstrate that the Step-Cycle model retains its complete expressive power even when restricted to (3, 1)-size void rules.

Comments

© 2026 The Author(s), under exclusive license to Springer Nature Switzerland AG

Recommended Citation

Luchsinger, Austin, Aiden Massie, Robert Schweller, Evan Tomai, and Tim Wylie. "Polynomial simulations of crn models with trimolecular void step-cycle crns." In International Conference on Unconventional Computation and Natural Computation, pp. 378-393. Cham: Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-032-15641-9_25

First Page

378

Last Page

393

Publication Title

International Conference on Unconventional Computation and Natural Computation

DOI

10.1007/978-3-032-15641-9_25