String tile models for DNA computing by self-assembly

Abstract

This paper investigates computation by linear assemblies of complex DNA tiles, which we call string tiles. By keeping track of the strands as they weave back and forth through the assembly, we show that surprisingly sophisticated calculations can be performed using linear self-assembly. Examples range from generating an addition table to providing O(1) solutions to CNF-SAT and DHPP. We classify the families of languages that can be generated by various types of DNA molecules, and establish a correspondence to the existing classes ET0Lml and ET0Lfin. Thus, linear self-assembly of string tiles can generate the output languages of finite-visit Turing Machines.