Testing Dynamic Environments: Back to Basics

Abstract: 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.