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
