Open Problems

The following are a list of open problems in self-assembly:

1) In his 1998 thesis , Winfree showed that the class of directed aTAM systems at temperature 2 is computationally universal, and in Cook et al. showed that undirected temperature 1 aTAM systems could perform computations with a given amount of certainty and that in 2 planes directed aTAM temperature 1 systems were computationally universal. Is the class of directed aTAM systems at temperature 1 in the plane computationally universal? In Doty, Patitz, and Summers provide deep insights into this question.

2) In , Doty et al. introduced a model known as the fuzzy temperature model and showed that in this model n by n squares could efficiently self-assemble. Can systems in this model also perform general computation?

3) In Doty et al. showed that the aTAM is intrinsically universal for itself, but for directed systems the intrinsically universal tile set fundamentally relies on nondeterminism. Is the class of directed aTAM systems intrinsically universal for itself?

4) Is the STAM intrinsically universal for itself?

5) Is the class of aTAM systems at temperature 1 intrinsically universal for itself?

6) In his 1998 thesis , Winfree introduced both the aTAM and its more practical counterpart the kTAM. Currently, the 2HAM does not have a more realistic counterpart. Formulate a "k2HAM" model which takes into account the size of assemblies binding together (the bigger the assemblies the less likely it is they will bind together) and the lack of rigidity when assemblies come together.

7) In Self-Assembly of Discrete Self-Similar Fractals, Patitz and Summers proved several results about self-assembling discrete self-similar fractals, but it is still an open questions as to whether or not there exists a discrete self-similar fractal that can be self-assembled in the aTAM.