Speaker
Description
The concept of input-independent computational time for chemistry-based analog computers was introduced in \cite{anderson2025arithmetic}, where it was shown that arithmetic operations can be computed in a fixed time independent of the input values. Here, by inputs we mean the numerical values encoded by the initial concentrations of designated input species, with the underlying reaction network and rate constants held fixed. Combining these operations via power series approximations to compute transcendental functions is possible in principle, but requires a number of chemical species that grows with respect to the number of terms retained.
In this talk we focus on two widely used transcendental functions, the exponential and logarithmic functions. We construct reaction network modules that compute these functions directly, without relying on truncated power series. We show that the resulting modules are mass-action systems, and prove that they achieve arbitrary accuracy given sufficient time while operating at input-independent speed. These two functions serve as foundational cases and are intended as building templates for computing more general transcendental functions via chemical reaction networks.
Bibliography
@article{anderson2025arithmetic,
title={Chemical mass-action systems as analog computers: Implementing arithmetic computations at specified speed},
author={Anderson, David F. and Joshi, Badal},
journal={Theoretical Computer Science},
volume={1025},
pages={114983},
year={2025},
publisher={Elsevier}
}
