{"id":"https://openalex.org/W4410090935","doi":"https://doi.org/10.1007/s11047-025-10015-y","title":"A directed graph allowing for the exploration of the set of number-conserving non-uniform one-dimensional binary cellular automata with radius one and half","display_name":"A directed graph allowing for the exploration of the set of number-conserving non-uniform one-dimensional binary cellular automata with radius one and half","publication_year":2025,"publication_date":"2025-05-05","ids":{"openalex":"https://openalex.org/W4410090935","doi":"https://doi.org/10.1007/s11047-025-10015-y"},"language":"en","primary_location":{"id":"doi:10.1007/s11047-025-10015-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-025-10015-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-025-10015-y.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/s11047-025-10015-y.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000165514","display_name":"Barbara Wolnik","orcid":"https://orcid.org/0000-0003-2935-5529"},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I40413290","display_name":"University of Gda\u0144sk","ror":"https://ror.org/011dv8m48","country_code":"PL","type":"education","lineage":["https://openalex.org/I40413290"]},{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE","PL"],"is_corresponding":true,"raw_author_name":"Barbara Wolnik","raw_affiliation_strings":["Department of Data Analysis and Mathematical Modelling, KERMIT, Faculty of Bioscience Engineering, Ghent University, Coupure Links 653, 9000, Gent, Belgium","Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gda\u0144sk, 80-308, Gda\u0144sk, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Data Analysis and Mathematical Modelling, KERMIT, Faculty of Bioscience Engineering, Ghent University, Coupure Links 653, 9000, Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gda\u0144sk, 80-308, Gda\u0144sk, Poland","institution_ids":["https://openalex.org/I40413290","https://openalex.org/I4210137370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077620316","display_name":"Maciej Dziemia\u0144czuk","orcid":"https://orcid.org/0000-0002-0553-7750"},"institutions":[{"id":"https://openalex.org/I40413290","display_name":"University of Gda\u0144sk","ror":"https://ror.org/011dv8m48","country_code":"PL","type":"education","lineage":["https://openalex.org/I40413290"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Maciej Dziemia\u0144czuk","raw_affiliation_strings":["Institute of Informatics, Faculty of Mathematics, Physics and Informatics, University of Gda\u0144sk, 80-308, Gda\u0144sk, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Informatics, Faculty of Mathematics, Physics and Informatics, University of Gda\u0144sk, 80-308, Gda\u0144sk, Poland","institution_ids":["https://openalex.org/I40413290"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035248678","display_name":"Bartosz Makuracki","orcid":"https://orcid.org/0000-0003-1102-6321"},"institutions":[{"id":"https://openalex.org/I40413290","display_name":"University of Gda\u0144sk","ror":"https://ror.org/011dv8m48","country_code":"PL","type":"education","lineage":["https://openalex.org/I40413290"]},{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Bartosz Makuracki","raw_affiliation_strings":["Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gda\u0144sk, 80-308, Gda\u0144sk, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gda\u0144sk, 80-308, Gda\u0144sk, Poland","institution_ids":["https://openalex.org/I40413290","https://openalex.org/I4210137370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012437460","display_name":"Bernard De Baets","orcid":"https://orcid.org/0000-0002-3876-620X"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Bernard De Baets","raw_affiliation_strings":["Department of Data Analysis and Mathematical Modelling, KERMIT, Faculty of Bioscience Engineering, Ghent University, Coupure Links 653, 9000, Gent, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Data Analysis and Mathematical Modelling, KERMIT, Faculty of Bioscience Engineering, Ghent University, Coupure Links 653, 9000, Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5000165514"],"corresponding_institution_ids":["https://openalex.org/I32597200","https://openalex.org/I40413290","https://openalex.org/I4210137370"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.604,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.83664028,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"24","issue":"3","first_page":"469","last_page":"482"},"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":0.9954000115394592,"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":0.9901000261306763,"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":0.7297248244285583},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6634451746940613},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.640602707862854},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.5418646335601807},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5376203656196594},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5296209454536438},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5146151781082153},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5021228790283203},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.41444700956344604},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41389259696006775},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36443930864334106},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34966588020324707},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.07957863807678223}],"concepts":[{"id":"https://openalex.org/C35527583","wikidata":"https://www.wikidata.org/wiki/Q189156","display_name":"Cellular automaton","level":2,"score":0.7297248244285583},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6634451746940613},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.640602707862854},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.5418646335601807},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5376203656196594},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5296209454536438},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5146151781082153},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5021228790283203},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41444700956344604},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41389259696006775},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36443930864334106},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34966588020324707},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.07957863807678223},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11047-025-10015-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-025-10015-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-025-10015-y.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"},{"id":"pmh:oai:archive.ugent.be:01K58WD4RYXDS7VTTTZJX1T3E6","is_oa":true,"landing_page_url":"http://hdl.handle.net/1854/LU-01K58WD4RYXDS7VTTTZJX1T3E6","pdf_url":"https://biblio.ugent.be/publication/01K58WD4RYXDS7VTTTZJX1T3E6/file/01K591SEYGH3G01AAQA5XPMR92.pdf","source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1572-9796","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s11047-025-10015-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-025-10015-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-025-10015-y.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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410090935.pdf","grobid_xml":"https://content.openalex.org/works/W4410090935.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W2001109406","https://openalex.org/W2006435955","https://openalex.org/W2020957336","https://openalex.org/W2022133825","https://openalex.org/W2022271016","https://openalex.org/W2028809393","https://openalex.org/W2039586611","https://openalex.org/W2138274182","https://openalex.org/W2199831635","https://openalex.org/W3157876618","https://openalex.org/W4232143575","https://openalex.org/W4315796302","https://openalex.org/W4386600590"],"related_works":["https://openalex.org/W2164619678","https://openalex.org/W2113544496","https://openalex.org/W2360313292","https://openalex.org/W2067777412","https://openalex.org/W1669105318","https://openalex.org/W2359527201","https://openalex.org/W2353714615","https://openalex.org/W9202957","https://openalex.org/W2370307662","https://openalex.org/W3091867061"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"main":[2],"obstacle":[3],"in":[4,113],"the":[5,13,21,25,31,41,55,71,89,104],"quest":[6],"for":[7],"non-uniform":[8,60,130],"cellular":[9,63,94,131],"automata":[10,64,95,132],"that":[11,82],"meet":[12],"often":[14],"desired":[15],"property":[16],"of":[17,24,33,43,57,73,77,91,106,133],"number":[18],"conservation":[19],"is":[20,84],"vast":[22],"size":[23],"search":[26],"space,":[27],"going":[28],"far":[29],"beyond":[30],"capabilities":[32],"today\u2019s":[34],"computers.":[35],"In":[36],"this":[37,134],"paper,":[38],"we":[39],"expound":[40],"construction":[42],"a":[44,74,85,97,125],"directed":[45,111],"graph":[46],"$$\\Pi":[47,114],"$$":[48,115],"<mml:math":[49,116],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[50,117],"<mml:mi>\u03a0</mml:mi>":[51,118],"</mml:math>":[52,119],"related":[53],"to":[54,128],"set":[56,90,105],"all":[58,92,107],"number-conserving":[59],"one-dimensional":[61],"binary":[62],"with":[65,100,124],"radius":[66],"one":[67],"and":[68,103],"half":[69],"(i.e.,":[70],"neighborhood":[72],"cell":[75],"consists":[76],"four":[78],"cells).":[79],"We":[80],"show":[81],"there":[83],"one-to-one":[86],"correspondence":[87],"between":[88],"such":[93],"on":[96],"finite":[98],"grid":[99],"n":[101,109],"cells":[102],"length-":[108],"closed":[110],"walks":[112],".":[120],"This":[121],"provides":[122],"us":[123],"powerful":[126],"tool":[127],"investigate":[129],"type.":[135]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-17T17:19:04.345684","created_date":"2025-10-10T00:00:00"}