par Chalk, Cameron;Martinez, Eric;Schweller, Robert R.T.;Vega, Luis;Winslow, Andrew 
;Wylie, Tim
Référence Leibniz international proceedings in informatics, 57, 26
Publication Publié, 2016-08
;Wylie, TimRéférence Leibniz international proceedings in informatics, 57, 26
Publication Publié, 2016-08
Article révisé par les pairs
| Résumé : | We analyze the number of stages, tiles, and bins needed to construct n × n squares and scaled shapes in the staged tile assembly model. In particular, we prove that there exists a staged system with b bins and t tile types assembling an n × n square using O(log n-tb-t log t/b2 + log log b/log t) stages and Ω(log n-tb-t log t/b2) are necessary or almost all n. F or a shape S, we prove O(K(S)-tb-t log t/b2 +log log b/log t) stages suffice and Ω(K(S)-tb-t-t log t/b2) are necessary or the assembly o a scaled version of S, where K(S) denotes the Kolmogorov complexity of S. Similarly tight bounds are also obtained when more powerful flexible glue functions are permitted. These are the first staged results that hold for all choices of b and t and generalize prior results. The upper bound constructions use a new technique for efficiently converting each both sources of system complexity, namely the tile types and mixing graph, into a "bit string" assembly. |
