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We consider a model of algorithmic self-assembly of geometric shapes out ofsquare Wang tiles studied in SODA 2010, in which there are two types of tiles(e.g., constructed out of DNA and RNA material) and one operation that destroysall tiles of a particular type (e.g., an RNAse enzyme destroys all RNA tiles).We show that a single use of this destruction operation enables much moreefficient construction of arbitrary shapes. In particular, an arbitrary shapecan be constructed using an asymptotically optimal number of distinct tiletypes (related to the shape's Kolmogorov complexity), after scaling the shapeby only a logarithmic factor. By contrast, without the destruction operation,the best such result has a scale factor at least linear in the size of theshape, and is connected only by a spanning tree of the scaled tiles. We alsocharacterize a large collection of shapes that can be constructed efficientlywithout any scaling.

Self-Assembly of Arbitrary Shapes Using RNAse Enzymes: Meeting the Kolmogorov Bound with Small Scale Factor (extended abstract)