{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T20:40:54Z","timestamp":1764794454216,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"Automata, Logic and Semantics","license":[{"start":{"date-parts":[[2017,9,15]],"date-time":"2017-09-15T00:00:00Z","timestamp":1505433600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,9,15]],"date-time":"2017-09-15T00:00:00Z","timestamp":1505433600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,9,15]],"date-time":"2017-09-15T00:00:00Z","timestamp":1505433600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["267356"],"award-info":[{"award-number":["267356"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100002341","name":"Research Council of Finland","doi-asserted-by":"crossref","award":["296018"],"award-info":[{"award-number":["296018"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>We discuss cellular automata over arbitrary finitely generated groups. We call a cellular automaton post-surjective if for any pair of asymptotic configurations, every pre-image of one is asymptotic to a pre-image of the other. The well known dual concept is pre-injectivity: a cellular automaton is pre-injective if distinct asymptotic configurations have distinct images. We prove that pre-injective, post-surjective cellular automata are reversible. Moreover, on sofic groups, post-surjectivity alone implies reversibility. We also prove that reversible cellular automata over arbitrary groups are balanced, that is, they preserve the uniform measure on the configuration space.<\/jats:p><jats:p>Comment: 16 pages, 3 figures, LaTeX &amp;quot;dmtcs-episciences&amp;quot; document class. Final   version for Discrete Mathematics and Theoretical Computer Science. Prepared   according to the editor's requests<\/jats:p>","DOI":"10.23638\/dmtcs-19-3-4","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:38:43Z","timestamp":1743698323000},"source":"Crossref","is-referenced-by-count":1,"title":["Post-surjectivity and balancedness of cellular automata over groups"],"prefix":"10.23638","volume":"Vol. 19 no. 3","author":[{"given":"Silvio","family":"Capobianco","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0670-6138","authenticated-orcid":false,"given":"Jarkko","family":"Kari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siamak","family":"Taati","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2017,9,15]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1507.02472v5","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1507.02472v5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:38:43Z","timestamp":1743698323000},"score":1,"resource":{"primary":{"URL":"http:\/\/dmtcs.episciences.org\/1485"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,15]]},"references-count":0,"journal-issue":{"issue":"Automata, Logic and Semantics","published-online":{"date-parts":[[2017,9,15]]}},"URL":"https:\/\/doi.org\/10.23638\/dmtcs-19-3-4","relation":{"has-preprint":[{"id-type":"arxiv","id":"1507.02472v4","asserted-by":"subject"},{"id-type":"arxiv","id":"1507.02472v3","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1507.02472","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1507.02472","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"type":"electronic","value":"1365-8050"}],"subject":[],"published":{"date-parts":[[2017,9,15]]},"article-number":"1485"}}