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When G is locally embeddable into finite groups (LEF), we show that the inverses of reversible algebraic cellular automata are automatically algebraic cellular automata and thus computable in polynomial time. Generalizations are also obtained for finite product Hopfian pointed object alphabets in concrete categories. Moreover, we prove that for algebraic cellular automata, the notions of reversibility and injectivity are equivalent whenever G is surjunctive and the field k is, additionally, uncountable of arbitrary characteristic. <\/jats:p>","DOI":"10.1142\/s021819672450053x","type":"journal-article","created":{"date-parts":[[2024,10,25]],"date-time":"2024-10-25T01:01:33Z","timestamp":1729818093000},"page":"31-47","source":"Crossref","is-referenced-by-count":1,"title":["LEF-groups and computability of reversible endomorphisms of symbolic varieties"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4347-8931","authenticated-orcid":false,"given":"Xuan Kien","family":"Phung","sequence":"first","affiliation":[{"name":"D\u00e9partement de Math\u00e9matiques et de Statistique, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al, Qu\u00e9bec, H3T 1J4, Canada"},{"name":"D\u00e9partement d\u2019informatique et de recherche op\u00e9rationnelle, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al, Qu\u00e9bec, H3T 1J4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,12,24]]},"reference":[{"key":"S021819672450053XBIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2007.06.035"},{"key":"S021819672450053XBIB002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7643-8412-8_3"},{"key":"S021819672450053XBIB003","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385708080437"},{"key":"S021819672450053XBIB004","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14034-1"},{"key":"S021819672450053XBIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2010.09.020"},{"key":"S021819672450053XBIB006","doi-asserted-by":"publisher","DOI":"10.1007\/978-88-470-2853-1_6"},{"key":"S021819672450053XBIB007","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2019.1602872"},{"key":"S021819672450053XBIB008","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.2020.306.31"},{"key":"S021819672450053XBIB009","first-page":"1","author":"Ceccherini-Silberstein T.","year":"2024","journal-title":"Ergodic Theory Dyn. 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