2021/05/03 by Nakar, Yonatan, Ron, Dana · 1 citation
#Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.2105.00759
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/ε) , 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/ε) -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.