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.
@InProceedings{nakar_et_al:LIPIcs.ICALP.2021.98, author = {Nakar, Yonatan and Ron, Dana}, title = {{Testing Dynamic Environments: Back to Basics}}, booktitle = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)}, pages = {98:1--98:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-195-5}, ISSN = {1868-8969}, year = {2021}, volume = {198}, editor = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.98}, URN = {urn:nbn:de:0030-drops-141672}, doi = {10.4230/LIPIcs.ICALP.2021.98}, annote = {Keywords: Property Testing} }
Feedback for Dagstuhl Publishing