Algorithmic self-assembly of dna
Algorithmic self-assembly of dna
Adding symbolic information to picture models: definitions and properties
Theoretical Computer Science
The Undecidability of the Infinite Ribbon Problem: Implications for Computing by Self-Assembly
SIAM Journal on Computing
Directed figure codes with weak equality
IDEAL'10 Proceedings of the 11th international conference on Intelligent data engineering and automated learning
Error free self-assembly using error prone tiles
DNA'04 Proceedings of the 10th international conference on DNA computing
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The process where simple entities form more complex structures acting autonomously is called self-assembly; it lies at the centre of many physical, chemical and biological phenomena. Massively parallel formation of nanostructures or DNA computation are just two examples of possible applications of self-assembly once it is technologically harnessed. Various mathematical models have been proposed for selfassembly, including the well-known Winfree's Tile Assembly Model based on Wang tiles on a two-dimensional plane. In the present paper we propose a model based on directed figures with partial catenation. Directed figures are defined as labelled polyominoes with designated start and end points, and catenation is defined for non-overlapping figures. This is one of possible extensions generalizing words and variable-length codes to planar structures, and a flexible model, allowing for a natural expression of self-assembling entities as well as e.g. image representation or "pictorial barcoding." We prove several undecidability results related to filling the plane with a given set of figures and formation of infinite and semiinfinite zippers, demonstrating a unifying approach that could be useful for the study of self-assembly.