David Doty

Theory of algorithmic self-assembly

The challenge of programming molecules to manipulate themselves.

Deterministic function computation with chemical reaction networks

Chemical reaction networks (CRNs) formally model chemistry in a well-mixed solution. CRNs are widely used to describe information processing occurring in natural cellular regulatory networks, and with upcoming advances in synthetic biology, CRNs are a promising language for the design of artificial molecular control circuitry. Nonetheless, despite the widespread use of CRNs in the natural sciences, the range of computational behaviors exhibited by CRNs is not well understood. CRNs have been shown to be efficiently Turing-universal (i.e., able to simulate arbitrary algorithms) when allowing for a small probability of error. CRNs that are guaranteed to converge on a correct answer, on the other hand, have been shown to decide only the semilinear predicates (a multi-dimensional generalization of “eventually periodic” sets). We introduce the notion of function, rather than predicate, computation by representing the output of a function

Randomized Self-Assembly for Exact Shapes

{f:{\mathbb{N}}^k\to{\mathbb{N}}^l}

INTRINSIC UNIVERSALITY IN SELF-ASSEMBLY

f:Nk→Nl by a count of some molecular species, i.e., if the CRN starts with

Speed Faults in Computation by Chemical Reaction Networks

x_1,\ldots,x_k

Stable leader election in population protocols requires linear time

x1,…,xk molecules of some “input” species