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Molecular self-assembly gives rise to a great diversity of complex forms, from crystals and DNA helices to microtubules and holoenzymes. We study a formal model of pseudo-crystalline self-assembly, called the Tile Assembly Model, in which a tile may be added to the growing object when the total interaction strength with its neighbors exceeds a parameter 7-.(More)
Algorithms and information, fundamental to technological and biological organization, are also an essential aspect of many elementary physical phenomena, such as molecular self-assembly. Here we report the molecular realization, using two-dimensional self-assembly of DNA tiles, of a cellular automaton whose update rule computes the binary function XOR and(More)
We introduce a new model of molecular computation that we call the sticker model. Like many previous proposals it makes use of DNA strands as the physical substrate in which information is represented and of separation by hybridization as a central mechanism. However, unlike previous models, the stickers model has a random access memory that requires no(More)
Self-assembly is the ubiquitous process by which simple objects autonomously assemble into intricate complexes. It has been suggested that intricate self-assembly processes will ultimately be used in circuit fabrication, nano-robotics, DNA computation, and amorphous computing. In this paper, we study two combinatorial optimization problems related to(More)
Self-assembly creates natural mineral, chemical, and biological structures of great complexity. Often, the same starting materials have the potential to form an infinite variety of distinct structures; information in a seed molecule can determine which form is grown as well as where and when. These phenomena can be exploited to program the growth of complex(More)
A 20-variable instance of the NP-complete three-satisfiability (3-SAT) problem was solved on a simple DNA computer. The unique answer was found after an exhaustive search of more than 1 million (2(20)) possibilities. This computational problem may be the largest yet solved by nonelectronic means. Problems of this size appear to be beyond the normal range of(More)
Copying and counting are useful primitive operations for computation and construction. We have made DNA crystals that copy and crystals that count as they grow. For counting, 16 oligonucleotides assemble into four DNA Wang tiles that subsequently crystallize on a polymeric nucleating scaffold strand, arranging themselves in a binary counting pattern that(More)