Article révisé par les pairs
Résumé : We consider problems in variations of the two-handed abstract Tile Assembly Model (2HAM), a generalization of Erik Winfree’s abstract Tile Assembly Model (aTAM).In the latter, tiles attach one-at-a-time to a seed-containing assembly.In the former, tiles aggregate into supertiles that then further combine to form larger supertiles; hence, constructions must be robust to the choice of seed (nucleation) tiles.We obtain three distinct results in two 2HAM variants whose aTAM siblings are well-studied.In the first variant, called the restricted glue 2HAM (rg2HAM), glue strengths are restricted to −1, 0, or 1.We prove this model is Turing universal, overcoming undesired growth by breaking apart undesired computation assembly via repulsive forces.In the second 2HAM variant, the 3D 2HAM (3D2HAM), tiles are (three-dimensional) cubes.We prove that assembling a (roughly twolayer) n × n square in this model is possible with O(log2 n) tile types.The construction uses “cyclic, colliding” binary counters, and assembles the shape non-deterministically.Finally, we prove that there exist 3D2HAM systems that only assemble infinite aperiodic shapes.