  We consider the problem of fault-tolerance in nanoscale algorithmic
self-assembly. We employ a variant of Winfree's abstract Tile Assembly Model
(aTAM), the two-handed aTAM, in which square "tiles" -- a model of molecules
constructed from DNA for the purpose of engineering self-assembled
nanostructures -- aggregate according to specific binding sites of varying
strengths, and in which large aggregations of tiles may attach to each other,
in contrast to the seeded aTAM, in which tiles aggregate one at a time to a
single specially-designated "seed" assembly. We focus on a major cause of
errors in tile-based self-assembly: that of unintended growth due to "weak"
strength-1 bonds, which if allowed to persist, may be stabilized by subsequent
attachment of neighboring tiles in the sense that at least energy 2 is now
required to break apart the resulting assembly; i.e., the errant assembly is
stable at temperature 2. We study a common self-assembly benchmark problem,
that of assembling an n x n square using O(log n) unique tile types, under the
two-handed model of self-assembly. Our main result achieves a much stronger
notion of fault-tolerance than those achieved previously. Arbitrary strength-1
growth is allowed (i.e., the temperature is "fuzzy" and may drift from 2 to 1
for arbitrarily long); however, any assembly that grows sufficiently to become
stable at temperature 2 is guaranteed to assemble at temperature 2 into the
correct final assembly of an n x n square. In other words, errors due to
insufficient attachment, which is the cause of errors studied in earlier papers
on fault-tolerance, are prevented absolutely in our main construction, rather
than only with high probability and for sufficiently small structures, as in
previous fault-tolerance studies.
