String tile models for DNA computing by self-assembly

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 ET0L_(ml) and ET0L_(fin). Thus, linear self-assembly of string tiles can generate the output languages of finite-visit Turing Machines

3D DNA Self-Assembly Model for Graph Vertex Coloring

DNA self-assembly technology has brought novel inspirations to the development of DNA computing Diversified computational models based on DNA self-assembly have been used to solve various NP problems. In this paper, a 3D DNA self-assembly model is presented to solve the Graph Vertex Coloring problem. With the capacity of DNA molecules in massive parallel computation, the model can simulate a non-deterministic algorithm and solve the problem in linear time Theta(n) The number of distinct tiles used in the model is Theta(k(2)), where k is the size of the color set For the vertex 3-coloring problem, the model requires only 22 types of distinct tiles. Our work makes a significant attempt for exploring the computational power of 3D DNA self-assembl

DNA-BASED SELF-ASSEMBLY AND NANOROBOTICS: THEORY AND EXPERIMENTS

We study the following fundamental questions in DNA-based self-assembly and nanorobotics: How to control errors in self-assembly? How to construct complex nanoscale objects in simpler ways? How to transport nanoscale objects in programmable manner? Fault tolerance in self-assembly: Fault tolerant self-assembly is important for nanofab-rication and nanocomputing applications. It is desirable to design compact error-resilient schemes that do not result in the increase in the original size of the assemblies. We present a comprehensive theory of compact error-resilient schemes for algorithmic self-assembly in two and three dimensions, and discuss the limitations and capabilities of redundancy based compact error correction schemes. New and powerful self-assembly model: We develop a reversible self-assembly model in which the glue strength between two juxtaposed tiles is a function of the time they have been in neighboring positions. Under our time-dependent glue model, we can rigorously study and demonstrate catalysis and self-replication in the tile assembly. We can assemble thin rectangles of size k × N using O