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Self-assembly is affected by high error rates due to incorrect tiles in nano-technology manufacturing. Tile sets that can heal (fully or partially) an erroneous assembly have been proposed. Self-healing requires growth to be restarted such that erroneous tiles can be removed and the correct tiles to bind to the aggregate. Punctures can be used for this purpose. The goal of this paper is to characterize an intentionally induced puncture (and its relevant properties) on an erroneous tile site in the assembly. This allows to propagate any newly generated error away from the source of growth (i.e. the seed tile), such that self-assembly can continue along specific directions. Different types of puncture are considered with respect to growth direction, error and aggregate types. Puncture resilience is analyzed using a new characterization metric; different tile sets are investigated in detail. Analytical and simulation results are provided.

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An assessment of the effectiveness of healing for error tolerance in DNA self-assembly tile sets for algorithmic/nano-manufacturing applications is presented. Initially, the conditions for correct binding of a tile to an existing aggregate are analysed using a Markovian approach; based on this analysis, it is proved that correct aggregation (as identified with a so-called ideal tile set) is not always met for the existing tile sets for nano-manufacturing. A metric for assessing tile sets for healing by utilising punctures is proposed. Tile sets are investigated and assessed with respect to features such as error (mismatched tile) movement, punctured area and bond types. Subsequently, it is shown that the proposed metric can comprehensively assess the healing effectiveness of a puncture type for a tile set and its capability to attain error tolerance for the desired pattern. Extensive simulation results are provided.