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Moreover, an algorithm of computing the rank of rule matrix with null boundary condition for von Neumann neighborhood is developed. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for two-dimensional cellular automata are obtained. <\/jats:p>","DOI":"10.1142\/s0218127423500657","type":"journal-article","created":{"date-parts":[[2023,5,25]],"date-time":"2023-05-25T07:50:50Z","timestamp":1685001050000},"source":"Crossref","is-referenced-by-count":0,"title":["Irreversibility of 2D Linear CA and Garden of Eden"],"prefix":"10.1142","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8690-4531","authenticated-orcid":false,"given":"Doston","family":"Jumaniyozov","sequence":"first","affiliation":[{"name":"Romanovsky Institute of Mathematics of Uzbekistan Academy of Sciences, Tashkent, Uzbekistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bakhrom","family":"Omirov","sequence":"additional","affiliation":[{"name":"National University of Uzbekistan, University Street 4, Tashkent 100174, Uzbekistan"},{"name":"Akfa University, Milliy Bog\u2019 Street 264, Tashkent 111221, Uzbekistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shovkat","family":"Redjepov","sequence":"additional","affiliation":[{"name":"Tashkent University of Information Technologies, Tashkent, Uzbekistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Selman","family":"Uguz","sequence":"additional","affiliation":[{"name":"University of Texas at Dallas, Richardson, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,5,24]]},"reference":[{"key":"S0218127423500657BIB001","first-page":"77","volume":"99","author":"Adamatzky A.","year":"1999","journal-title":"Appl. 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