  We continue the line of work initiated by Goldreich and Ron (Journal of the
ACM, 2017) on testing dynamic environments and propose to pursue a systematic
study of the complexity of testing basic dynamic environments and local rules.
As a first step, in this work we focus on dynamic environments that correspond
to elementary cellular automata that evolve according to threshold rules.
  Our main result is the identification of a set of conditions on local rules,
and a meta-algorithm that tests evolution according to local rules that satisfy
the conditions. The meta-algorithm has query complexity poly$ (1/\epsilon) $,
is non-adaptive and has one-sided error. We show that all the threshold rules
satisfy the set of conditions, and therefore are poly$ (1/\epsilon) $-testable.
We believe that this is a rich area of research and suggest a variety of open
problems and natural research directions that may extend and expand our
results.
