mechanism of cooperative bindings. They replace each tile type by a k X k block of tile types such that ifan erroneous tile is incorporated in the assembly, there cannot be further growth without additional tilemismatches (see figure 8 for an example). Thus, assemblies with incorrect tiles grow much slower andallow more time for the erroneous attachments to dissociate before the error is locked into place. Thisproofreading can reduce error rates by a square factor over tile sets that do not implementproofreading. However, there is an inherent scale blow-up associated with this technique. Reif et al.(2004) eliminated this scale blow-up by giving a compact method to perform proofreading. While theseschemes reduce cooperative binding errors they do not protect against facet nucleation errors and donot scale well with increased k. Chen and Goel (2005) introduced the snaked-proofreading techniquethat guards against both cooperative binding and facet nucleation errors and proved that error ratesdrop exponentially as a function of k. Both conventional and snaked-proofreading systems wereexperimentally tested out in Chen et al. (2007) and a 2 x 2 snaked-proofreading system was shown toreduce facet nucleation errors four-fold as compared to the conventional proofreading technique.
Figure 8: Proofreading for Sierpinski tiling, Winfree and Bekbolatov (2003)Snaked-proofreading reintroduces the problem of scale blow-up, but Soloveichik and Winfree (2006) fixthis by describing a compact method to implement it. The drawback is that for certain patterns thisresults in an exponential blow-up in the descriptional complexity of the pattern (as measured by thenumber of tile types that assemble it). Figure 9: Snaked-proofreading Chen and Goel (2005)Given a tile set, what are the relative concentrations of tile types that minimize errors? Chen and Kao(2011) prove that for rectilinear patterns, carefully setting the concentrations of tile types allows one toachieve minimum errors with fastest possible assembly time. Instead of working with static tiles, one 5. Experimental advances in purely hybridization based computation
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