{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T09:26:45Z","timestamp":1758274005945,"version":"3.41.2"},"reference-count":28,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T00:00:00Z","timestamp":1559433600000},"content-version":"vor","delay-in-days":152,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871280","11471003"],"award-info":[{"award-number":["11871280","11471003"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>The All\u2010Ones Problem comes from the theory of <jats:italic>\u03c3<\/jats:italic><jats:sup>+<\/jats:sup>\u2010automata, which is related to graph dynamical systems as well as the Odd Set Problem in linear decoding. In this paper, we further study and compute the solutions to the \u201cAll\u2010Colors Problem,\u201d a generalization of \u201cAll\u2010Ones Problem,\u201d on some interesting classes of graphs which can be divided into two subproblems: Strong\u2010All\u2010Colors Problem and Weak\u2010All\u2010Colors Problem, respectively. We also introduce a new kind of All\u2010Colors Problem, <jats:italic>k<\/jats:italic>\u2010Random Weak\u2010All\u2010Colors Problem, which is relevant to both combinatorial number theory and cellular automata theory.<\/jats:p>","DOI":"10.1155\/2019\/3164692","type":"journal-article","created":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T23:32:13Z","timestamp":1559518333000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Solutions to All\u2010Colors Problem on Graph Cellular Automata"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2224-1484","authenticated-orcid":false,"given":"Xiaoyan","family":"Zhang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0073-9791","authenticated-orcid":false,"given":"Chao","family":"Wang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2019,6,2]]},"reference":[{"key":"e_1_2_9_1_2","first-page":"1803","article-title":"Graph dynamical systems with general boolean states","volume":"9","author":"Aledo J. 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