Robust Real-Time Computing with Chemical Reaction Networks

Recent research into analog computing has introduced new notions of real numbers. Huang, Klinge, Lathrop, Li, and Lutz defined a notion numbers in real-time with chemical reaction networks (CRNs), introducing the classes $\mathbb{R}_\text{LCRN}$ (the class all Lyapunov CRN-computable numbers) $\mathbb{R}_\text{RTCRN}$ numbers). In their paper, they show inclusion algebraic $ALG \subseteq \mathbb{R}_\text{LCRN} \mathbb{R}_\text{RTCRN}$ that \subsetneqq but leave open where is proper. this we resolve problem $ALG= \mathbb{R}_\text{RTCRN}$. However, definition computation fragile sense it sensitive to perturbations initial conditions. To flaw, further require CRN withstand these perturbations. doing so, arrive at discrete model memory. This approach several benefits. First, bounded may compute values approximately finite time. Second, can tolerate small its species' concentrations. Third, taking measurement CRN's state only requires precision proportional exactness approximations. Lastly, if memory, Turing machines are equivalent under simulations.