Abstract
The paper reviews two computing models by DNA self-assembly whose proof of principal have recently been experimentally confirmed. The first model incorporates DNA nano-devices and triple crossover DNA molecules to algorithmically arrange non-DNA species. This is achieved by simulating a finite-state automaton with output where golden nanoparticles are assembled to read-out the result. In the second model, a complex DNA molecule representing a graph emerges as a solution of a computational problem. This supports the idea that in molecular self-assembly computing, it may be necessary to develop the notion of shape processing besides the classical approach through symbol processing.