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DNA tiles provide a promising technique for assembling structures with nanoscale resolution through self-assembly by basic interactions rather than top-down assembly of individual structures. Tile systems can be programmed to grow based on logical rules, allowing for a small number of tile types to assemble large, complex assemblies that can retain nanoscale resolution. Such algorithmic systems can even assemble different structures using the same tiles, based on inputs that seed the growth. While programming and theoretical analysis of tile self-assembly often makes use of abstract logical models of growth, experimentally implemented systems are governed by nanoscale physical processes that can lead to very different behavior, more accurately modeled by taking into account the thermodynamics and kinetics of tile attachment and detachment in solution. This review discusses the relationships between more abstract and more physically realistic tile assembly models. A central concern is how consideration of model differences enables the design of tile systems that robustly exhibit the desired abstract behavior in realistic physical models and in experimental implementations. Conversely, we identify situations where self-assembly in abstract models can not be well-approximated by physically realistic models, putting constraints on physical relevance of the abstract models. To facilitate the discussion, we introduce a unified model of tile self-assembly that clarifies the relationships between several well-studied models in the literature. Throughout, we highlight open questions regarding the physical principles for DNA tile self-assembly.

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