RevCRN: Reversible Analog Computation using Chemical Reaction Networks
Abstract
The computability of real numbers and functions using Turing Machines has been a central area of theoretical computer science since the mid-20th century. In the late 20th century, it was shown that chemical reactions can serve as a basis for computation using the Chemical Reaction Network (CRN) model. Recent advances in computing real numbers using Deterministic Chemical Reaction Networks (DCRNs) have identified numerous classes of DCRN-computable real numbers. In parallel, the works of R. Landauer and C. H. Bennett, spanning the 1960s to the early 2000s, showed that reversible computing offers significant advantages over irreversible methods, particularly in energy efficiency, motivating extensive research on reversible computation. In this work, we investigate the computability of real numbers using Reversible Chemical Reaction Networks (RevCRNs). The paper has two primary contributions: (1) establishing relationships among CRN-computable real number classes including Lyapunov CRN (ℝLCRN), Real-Time CRN (ℝRTCRN), rational numbers (ℚ), and RevCRNs (ℝRevCRN), with key results: (i) ℚ is a strict subset of ℝRevCRN; (ii) the set of positive algebraic numbers (ALG), ℝLCRN, and real numbers computable by 1-species RevCRN (ℝRevCRN1s) are equal; (iii) ℝRTCRN and ℝRevCRN exhibit non-empty overlap; and (iv) the set of real numbers computable by detailed-balanced RevCRNs (ℝDetBalRevCRN) is a subset of ALG; and (2) exploring the existence of a hierarchy within ℝRevCRN. Finally, we leave open the exact relationship between ℝRevCRN and ℝRTCRN while conjecturing a general hierarchy of RevCRN-computable reals.
Related
- Input-to-state stability of chemical reaction networks with application to molecular computation
- Simulation-free approximate Bayesian computation for stochastic reaction networks
- Bulk stability of bimolecular stochastic chemical reaction networks
- Joint Neural Posterior Estimation and Model Selection for Chemical Reaction Networks
- Optimal Control of Chemical Reaction Networks with Thermodynamic Cost
BibTeX
@misc{biswas2026revcrn,
title = {{RevCRN: Reversible Analog Computation using Chemical Reaction Networks}},
author = {Saptarshi Biswas and James I. Lathrop and Rana D. Parshad},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.11362},
eprint = {2608.11362},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.11362},
}
RIS
TY - UNPB
TI - RevCRN: Reversible Analog Computation using Chemical Reaction Networks
AU - Saptarshi Biswas
AU - James I. Lathrop
AU - Rana D. Parshad
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2608.11362
UR - https://arxiv.org/abs/2608.11362
AB - The computability of real numbers and functions using Turing Machines has been a central area of theoretical computer science since the mid-20th century. In the late 20th century, it was shown that chemical reactions can serve as a basis for computation using the Chemical Reaction Network (CRN) model. Recent advances in computing real numbers using Deterministic Chemical Reaction Networks (DCRNs) have identified numerous classes of DCRN-computable real numbers. In parallel, the works of R. Landauer and C. H. Bennett, spanning the 1960s to the early 2000s, showed that reversible computing offers significant advantages over irreversible methods, particularly in energy efficiency, motivating extensive research on reversible computation. In this work, we investigate the computability of real numbers using Reversible Chemical Reaction Networks (RevCRNs). The paper has two primary contributions: (1) establishing relationships among CRN-computable real number classes including Lyapunov CRN (ℝ_LCRN), Real-Time CRN (ℝ_RTCRN), rational numbers (ℚ), and RevCRNs (ℝ_RevCRN), with key results: (i) ℚ is a strict subset of ℝ_RevCRN; (ii) the set of positive algebraic numbers (ALG), ℝ_LCRN, and real numbers computable by 1-species RevCRN (ℝ_RevCRN^1s) are equal; (iii) ℝ_RTCRN and ℝ_RevCRN exhibit non-empty overlap; and (iv) the set of real numbers computable by detailed-balanced RevCRNs (ℝ^DetBal_RevCRN) is a subset of ALG; and (2) exploring the existence of a hierarchy within ℝ_RevCRN. Finally, we leave open the exact relationship between ℝ_RevCRN and ℝ_RTCRN while conjecturing a general hierarchy of RevCRN-computable reals.
ER -