{"id":"https://openalex.org/W7128913298","doi":"https://doi.org/10.1007/s11047-026-10067-8","title":"On the surjunctivity and the Garden of Eden theorem for non-uniform cellular automata","display_name":"On the surjunctivity and the Garden of Eden theorem for non-uniform cellular automata","publication_year":2026,"publication_date":"2026-02-14","ids":{"openalex":"https://openalex.org/W7128913298","doi":"https://doi.org/10.1007/s11047-026-10067-8"},"language":"en","primary_location":{"id":"doi:10.1007/s11047-026-10067-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-026-10067-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-026-10067-8.pdf","source":{"id":"https://openalex.org/S149828480","display_name":"Natural Computing","issn_l":"1567-7818","issn":["1567-7818","1572-9796"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Natural Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11047-026-10067-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5124402218","display_name":"Katariina Paturi","orcid":null},"institutions":[{"id":"https://openalex.org/I155660961","display_name":"University of Turku","ror":"https://ror.org/05vghhr25","country_code":"FI","type":"education","lineage":["https://openalex.org/I155660961"]},{"id":"https://openalex.org/I16231767","display_name":"Turku University of Applied Sciences","ror":"https://ror.org/04s0yt949","country_code":"FI","type":"education","lineage":["https://openalex.org/I16231767"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Katariina Paturi","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Turku, Vesilinnantie 5, 20014, Turku, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Turku, Vesilinnantie 5, 20014, Turku, Finland","institution_ids":["https://openalex.org/I155660961","https://openalex.org/I16231767"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057995798","display_name":"Jarkko Kari","orcid":"https://orcid.org/0000-0003-0670-6138"},"institutions":[{"id":"https://openalex.org/I155660961","display_name":"University of Turku","ror":"https://ror.org/05vghhr25","country_code":"FI","type":"education","lineage":["https://openalex.org/I155660961"]},{"id":"https://openalex.org/I16231767","display_name":"Turku University of Applied Sciences","ror":"https://ror.org/04s0yt949","country_code":"FI","type":"education","lineage":["https://openalex.org/I16231767"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Jarkko Kari","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Turku, Vesilinnantie 5, 20014, Turku, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Turku, Vesilinnantie 5, 20014, Turku, Finland","institution_ids":["https://openalex.org/I155660961","https://openalex.org/I16231767"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5124402218"],"corresponding_institution_ids":["https://openalex.org/I155660961","https://openalex.org/I16231767"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3211874,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":"1","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":0.978600025177002,"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":0.978600025177002,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.00279999990016222,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.0020000000949949026,"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/garden-of-eden","display_name":"Garden of Eden","score":0.8385000228881836},{"id":"https://openalex.org/keywords/cellular-automaton","display_name":"Cellular automaton","score":0.7965999841690063},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6718000173568726},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5863000154495239},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.48489999771118164},{"id":"https://openalex.org/keywords/continuous-spatial-automaton","display_name":"Continuous spatial automaton","score":0.4580000042915344}],"concepts":[{"id":"https://openalex.org/C2779468979","wikidata":"https://www.wikidata.org/wiki/Q1974793","display_name":"Garden of Eden","level":2,"score":0.8385000228881836},{"id":"https://openalex.org/C35527583","wikidata":"https://www.wikidata.org/wiki/Q189156","display_name":"Cellular automaton","level":2,"score":0.7965999841690063},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6718000173568726},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6689000129699707},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5863000154495239},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5074999928474426},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.48489999771118164},{"id":"https://openalex.org/C75745568","wikidata":"https://www.wikidata.org/wiki/Q5165519","display_name":"Continuous spatial automaton","level":5,"score":0.4580000042915344},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.415800005197525},{"id":"https://openalex.org/C108882938","wikidata":"https://www.wikidata.org/wiki/Q274506","display_name":"Uniform distribution (continuous)","level":2,"score":0.33649998903274536},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31459999084472656},{"id":"https://openalex.org/C192499940","wikidata":"https://www.wikidata.org/wiki/Q17022326","display_name":"Stochastic cellular automaton","level":3,"score":0.29330000281333923},{"id":"https://openalex.org/C116248031","wikidata":"https://www.wikidata.org/wiki/Q214526","display_name":"Automata theory","level":3,"score":0.2874000072479248},{"id":"https://openalex.org/C50348692","wikidata":"https://www.wikidata.org/wiki/Q6887056","display_name":"Mobile automaton","level":4,"score":0.2556000053882599}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11047-026-10067-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-026-10067-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-026-10067-8.pdf","source":{"id":"https://openalex.org/S149828480","display_name":"Natural Computing","issn_l":"1567-7818","issn":["1567-7818","1572-9796"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Natural Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11047-026-10067-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-026-10067-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-026-10067-8.pdf","source":{"id":"https://openalex.org/S149828480","display_name":"Natural Computing","issn_l":"1567-7818","issn":["1567-7818","1572-9796"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Natural Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323313","display_name":"Turun Yliopisto","ror":"https://ror.org/05vghhr25"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7128913298.pdf"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W181454903","https://openalex.org/W1987542250","https://openalex.org/W2006435955","https://openalex.org/W2020957336","https://openalex.org/W2022271016","https://openalex.org/W4252285110","https://openalex.org/W4292512159","https://openalex.org/W4295763127"],"related_works":[],"abstract_inverted_index":{"Non-uniform":[0],"cellular":[1,8],"automata":[2,9],"(NUCA)":[3],"are":[4],"an":[5],"extension":[6],"of":[7,23,37,54,67],"with":[10],"multiple":[11],"local":[12,24,55],"rules":[13,25,56],"in":[14,31],"different":[15],"cells.":[16],"We":[17,41],"show":[18,43,72],"that":[19,44,57,73],"if":[20],"the":[21,32,35,65],"distribution":[22,77,81],"is":[26,51],"uniformly":[27],"recurrent,":[28],"or":[29],"recurrent":[30,80],"one-dimensional":[33,47,75],"case,":[34],"Garden":[36,66],"Eden":[38,68],"theorem":[39],"holds.":[40],"also":[42],"for":[45],"any":[46],"non-recurrent":[48],"distribution,":[49],"there":[50],"a":[52,59,74,83],"substitution":[53],"defines":[58,82],"NUCA":[60],"which":[61],"does":[62],"not":[63],"satisfy":[64],"theorem.":[69],"Finally,":[70],"we":[71],"rule":[76],"asymptotic":[78],"to":[79],"surjunctive":[84],"NUCA.":[85]},"counts_by_year":[],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2026-02-15T00:00:00"}