{"id":"https://openalex.org/W4378227588","doi":"https://doi.org/10.1142/s0218127423500657","title":"Irreversibility of 2D Linear CA and Garden of Eden","display_name":"Irreversibility of 2D Linear CA and Garden of Eden","publication_year":2023,"publication_date":"2023-05-01","ids":{"openalex":"https://openalex.org/W4378227588","doi":"https://doi.org/10.1142/s0218127423500657"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127423500657","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218127423500657","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064844969","display_name":"Doston Jumaniyozov","orcid":"https://orcid.org/0000-0002-8690-4531"},"institutions":[{"id":"https://openalex.org/I1302269238","display_name":"Academy of Sciences Republic of Uzbekistan","ror":"https://ror.org/01xgfaw76","country_code":"UZ","type":"government","lineage":["https://openalex.org/I1302269238"]}],"countries":["UZ"],"is_corresponding":true,"raw_author_name":"Doston Jumaniyozov","raw_affiliation_strings":["Romanovsky Institute of Mathematics of Uzbekistan Academy of Sciences, Tashkent, Uzbekistan"],"raw_orcid":"https://orcid.org/0000-0002-8690-4531","affiliations":[{"raw_affiliation_string":"Romanovsky Institute of Mathematics of Uzbekistan Academy of Sciences, Tashkent, Uzbekistan","institution_ids":["https://openalex.org/I1302269238"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036779291","display_name":"B. A. Omirov","orcid":"https://orcid.org/0000-0002-5821-4365"},"institutions":[{"id":"https://openalex.org/I4210096951","display_name":"Central Asian University","ror":"https://ror.org/00x6wnm78","country_code":"UZ","type":"education","lineage":["https://openalex.org/I4210096951"]},{"id":"https://openalex.org/I47151758","display_name":"National University of Uzbekistan","ror":"https://ror.org/011647w73","country_code":"UZ","type":"education","lineage":["https://openalex.org/I47151758"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Bakhrom Omirov","raw_affiliation_strings":["Akfa University, Milliy Bog\u2019 Street 264, Tashkent 111221, Uzbekistan","National University of Uzbekistan, University Street 4, Tashkent 100174, Uzbekistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Akfa University, Milliy Bog\u2019 Street 264, Tashkent 111221, Uzbekistan","institution_ids":["https://openalex.org/I4210096951"]},{"raw_affiliation_string":"National University of Uzbekistan, University Street 4, Tashkent 100174, Uzbekistan","institution_ids":["https://openalex.org/I47151758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012971571","display_name":"Shovkat Redjepov","orcid":"https://orcid.org/0000-0001-5293-3548"},"institutions":[{"id":"https://openalex.org/I21256249","display_name":"Tashkent University of Information Technology","ror":"https://ror.org/05987a729","country_code":"UZ","type":"education","lineage":["https://openalex.org/I21256249"]}],"countries":["UZ"],"is_corresponding":false,"raw_author_name":"Shovkat Redjepov","raw_affiliation_strings":["Tashkent University of Information Technologies, Tashkent, Uzbekistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tashkent University of Information Technologies, Tashkent, Uzbekistan","institution_ids":["https://openalex.org/I21256249"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049354782","display_name":"Selman U\u01e7uz","orcid":"https://orcid.org/0000-0003-3800-2389"},"institutions":[{"id":"https://openalex.org/I162577319","display_name":"The University of Texas at Dallas","ror":"https://ror.org/049emcs32","country_code":"US","type":"education","lineage":["https://openalex.org/I162577319"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Selman Uguz","raw_affiliation_strings":["University of Texas at Dallas, Richardson, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas at Dallas, Richardson, USA","institution_ids":["https://openalex.org/I162577319"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5064844969"],"corresponding_institution_ids":["https://openalex.org/I1302269238"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11112222,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"06","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9836000204086304,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cellular-automaton","display_name":"Cellular automaton","score":0.851081132888794},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.8339582681655884},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6844354271888733},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4976101219654083},{"id":"https://openalex.org/keywords/null","display_name":"Null (SQL)","score":0.47719988226890564},{"id":"https://openalex.org/keywords/von-neumann-architecture","display_name":"Von Neumann architecture","score":0.46996399760246277},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4517703056335449},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.45059239864349365},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4377915859222412},{"id":"https://openalex.org/keywords/abelian-sandpile-model","display_name":"Abelian sandpile model","score":0.42594006657600403},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4205547571182251},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4189506471157074},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4111034870147705},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3990269601345062},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1806568205356598},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1748165786266327},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14458659291267395},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.10920348763465881},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07423657178878784}],"concepts":[{"id":"https://openalex.org/C35527583","wikidata":"https://www.wikidata.org/wiki/Q189156","display_name":"Cellular automaton","level":2,"score":0.851081132888794},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.8339582681655884},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6844354271888733},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4976101219654083},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.47719988226890564},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.46996399760246277},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4517703056335449},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.45059239864349365},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4377915859222412},{"id":"https://openalex.org/C52359947","wikidata":"https://www.wikidata.org/wiki/Q4666685","display_name":"Abelian sandpile model","level":2,"score":0.42594006657600403},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4205547571182251},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4189506471157074},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4111034870147705},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3990269601345062},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1806568205356598},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1748165786266327},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14458659291267395},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.10920348763465881},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07423657178878784},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127423500657","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218127423500657","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.75}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W142045744","https://openalex.org/W1678052459","https://openalex.org/W1968720345","https://openalex.org/W1972863133","https://openalex.org/W1979559241","https://openalex.org/W1985762172","https://openalex.org/W1994519856","https://openalex.org/W1996095705","https://openalex.org/W2000270556","https://openalex.org/W2014149883","https://openalex.org/W2015702911","https://openalex.org/W2036424138","https://openalex.org/W2070832294","https://openalex.org/W2087973701","https://openalex.org/W2107774160","https://openalex.org/W2108704847","https://openalex.org/W2346054753","https://openalex.org/W4252285110","https://openalex.org/W4254434123"],"related_works":["https://openalex.org/W2090824337","https://openalex.org/W2921498481","https://openalex.org/W2963371116","https://openalex.org/W2022920970","https://openalex.org/W2112911989","https://openalex.org/W2117548279","https://openalex.org/W2165425090","https://openalex.org/W2120101606","https://openalex.org/W2149679937","https://openalex.org/W1972167486"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,9],"consider":[4],"a":[5],"pentagonal":[6],"lattice":[7],"and":[8,36,62],"investigate":[10],"the":[11,23,45,66],"rule":[12,48],"matrix":[13,49],"with":[14,22,50],"null":[15,51],"boundary":[16,52],"condition":[17,53],"for":[18,54,65,73],"two-dimensional":[19,74],"cellular":[20,75],"automata":[21,76],"field":[24],"[Formula:":[25,33],"see":[26,34],"text]":[27],"(the":[28],"set":[29],"of":[30,43,47,68,70],"integers":[31],"modulo":[32],"text])":[35],"analyze":[37],"their":[38],"characteristics.":[39],"Moreover,":[40],"an":[41],"algorithm":[42],"computing":[44],"rank":[46],"von":[55],"Neumann":[56],"neighborhood":[57],"is":[58],"developed.":[59],"Finally,":[60],"necessary":[61],"sufficient":[63],"conditions":[64],"existence":[67],"Garden":[69],"Eden":[71],"configurations":[72],"are":[77],"obtained.":[78]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
