Speaker
Description
Can a test tube compute? And if so, can it compute with the same efficiency over a wide range of inputs? Recent advances in synthetic biology have made it possible to deploy chemical reactions that implement computation inside a cell. Chemical reactions function as analog computers — they are ideally suited for solving differential equations and interface naturally with real-world analog signals. However, exact arithmetic on an analog computer presents novel challenges: in existing approaches the computation time can depend on the input, in some cases resulting in impractically slow computation.
We will discuss novel algorithms that address this issue. First, we present algorithms that perform arithmetic operations — identification, inversion, addition, multiplication, absolute difference, rectified subtraction, and nth roots — at input-independent speed, with the striking property that computation time does not scale with the number of elementary steps, a consequence of the inherently parallel nature of chemical computation. We then extend this program to transcendental functions, constructing reaction network modules for the exponential and logarithm that achieve arbitrary accuracy at input-independent speed without relying on truncated power series — the logarithm presenting significantly deeper mathematical challenges. Finally, we present a fractional (ratio) representation of numbers under which arithmetic becomes instantaneous — the encoded output is correct at every positive time.
