{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:24:15Z","timestamp":1777645455942,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2016,5,3]],"date-time":"2016-05-03T00:00:00Z","timestamp":1462233600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2016,5,3]]},"abstract":"<jats:p>The understanding of how predefined computations can be attained by means of individual cellular automata rules, their spatial arrangements or their temporal sequences, is a key conceptual underpinning in the general notion of emergent computation. In this context, here we construct a solution to the MOD n problem, which is the determination of whether the number of 1-bits in a cyclic binary string is perfectly divisible by the integer n &gt; 1. Our solution is given for any lattice size N that is co-prime to n, and relies upon a set of one-dimensional rules, with maximum radius of n \u2212 1, organised in a temporal sequence. Although the simpler cases of the problem for n = 2 and n = 3 have been addressed in the literature, this is the first account on the general case, for arbitrary n.<\/jats:p>","DOI":"10.3233\/fi-2016-1344","type":"journal-article","created":{"date-parts":[[2016,5,3]],"date-time":"2016-05-03T16:49:01Z","timestamp":1462294141000},"page":"1-17","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Computing Modulo-\n                    <i>n<\/i>\n                    by Composing Cellular Automata Rules"],"prefix":"10.1177","volume":"145","author":[{"given":"Claudio L.M.","family":"Martins","sequence":"first","affiliation":[{"name":"P\u00f3s-Gradua\u00e7\u00e3o em Engenharia El\u00e9trica e Computa\u00e7\u00e3o, Universidade Presbiteriana Mackenzie, S\u00e3o Paulo, SP - Brazil. ,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pedro P.B.","family":"de Oliveira","sequence":"additional","affiliation":[{"name":"P\u00f3s-Gradua\u00e7\u00e3o em Engenharia El\u00e9trica e Computa\u00e7\u00e3o, Universidade Presbiteriana Mackenzie, S\u00e3o Paulo, SP - Brazil. ,"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2016,5,3]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2016-1344","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2016-1344","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:32:16Z","timestamp":1777444336000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2016-1344"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,3]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,5,3]]}},"alternative-id":["10.3233\/FI-2016-1344"],"URL":"https:\/\/doi.org\/10.3233\/fi-2016-1344","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,5,3]]}}}