  Behaviors of Winfree's tile assembly systems (TASs) at high temperatures are
investigated in combination with integer programming of a specific form called
threshold programming. First, we propose a way to build bridges from the
Boolean satisfiability problem (SAT) to threshold programming, and further to
TAS's behavior, in order to prove the NP-hardness of optimizing temperatures of
TASs that behave in a way given as input. These bridges will take us further to
two important results on the behavior of TASs at high temperatures. The first
says that arbitrarily high temperatures are required to assemble some shape by
a TAS of "reasonable" size. The second is that for any temperature at least 4
given as a parameter, it is NP-hard to find the minimum size TAS that
self-assembles a given shape and works at the given temperature or below.
