{"id":"https://openalex.org/W2016156138","doi":"https://doi.org/10.1142/s0218127407019925","title":"EXTENDING CHUA'S GLOBAL EQUIVALENCE THEOREM ON WOLFRAM'S NEW KIND OF SCIENCE","display_name":"EXTENDING CHUA'S GLOBAL EQUIVALENCE THEOREM ON WOLFRAM'S NEW KIND OF SCIENCE","publication_year":2007,"publication_date":"2007-12-01","ids":{"openalex":"https://openalex.org/W2016156138","doi":"https://doi.org/10.1142/s0218127407019925","mag":"2016156138"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127407019925","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407019925","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/A5076993954","display_name":"Junbiao Guan","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JUNBIAO GUAN","raw_affiliation_strings":["Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101088187","display_name":"Shaowei Shen","orcid":null},"institutions":[{"id":"https://openalex.org/I75059550","display_name":"Zhejiang Gongshang University","ror":"https://ror.org/0569mkk41","country_code":"CN","type":"education","lineage":["https://openalex.org/I75059550"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"SHAOWEI SHEN","raw_affiliation_strings":["College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, Zhejiang 310000, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, Zhejiang 310000, P. R. China","institution_ids":["https://openalex.org/I75059550"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067116677","display_name":"Changbing Tang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210127700","display_name":"Zhejiang Shuren University","ror":"https://ror.org/0331z5r71","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210127700"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"CHANGBING TANG","raw_affiliation_strings":["Department of Basic Courses, Zhejiang Shuren University, Hangzhou, Zhejiang 310015, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Basic Courses, Zhejiang Shuren University, Hangzhou, Zhejiang 310015, P. R. China","institution_ids":["https://openalex.org/I4210127700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088079072","display_name":"Fangyue Chen","orcid":"https://orcid.org/0000-0002-5440-3206"},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"FANGYUE CHEN","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","institution_ids":["https://openalex.org/I135237710"]},{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, P. R. China","institution_ids":["https://openalex.org/I135237710"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.5232,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.95883965,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"17","issue":"12","first_page":"4245","last_page":"4259"},"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":0.9973999857902527,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9853000044822693,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.7642990350723267},{"id":"https://openalex.org/keywords/symbolic-dynamics","display_name":"Symbolic dynamics","score":0.6990728974342346},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6979578733444214},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5564480423927307},{"id":"https://openalex.org/keywords/topological-conjugacy","display_name":"Topological conjugacy","score":0.5084444880485535},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4932686686515808},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45387381315231323},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.44709062576293945},{"id":"https://openalex.org/keywords/cellular-automaton","display_name":"Cellular automaton","score":0.4338947832584381},{"id":"https://openalex.org/keywords/equivalence-class","display_name":"Equivalence class (music)","score":0.41523343324661255},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.4135768413543701},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13466650247573853},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09443026781082153},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06034824252128601}],"concepts":[{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.7642990350723267},{"id":"https://openalex.org/C16101541","wikidata":"https://www.wikidata.org/wiki/Q1350838","display_name":"Symbolic dynamics","level":2,"score":0.6990728974342346},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6979578733444214},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5564480423927307},{"id":"https://openalex.org/C165263651","wikidata":"https://www.wikidata.org/wiki/Q2443460","display_name":"Topological conjugacy","level":2,"score":0.5084444880485535},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4932686686515808},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45387381315231323},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.44709062576293945},{"id":"https://openalex.org/C35527583","wikidata":"https://www.wikidata.org/wiki/Q189156","display_name":"Cellular automaton","level":2,"score":0.4338947832584381},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.41523343324661255},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4135768413543701},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13466650247573853},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09443026781082153},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06034824252128601},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127407019925","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407019925","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W2001109406","https://openalex.org/W2037830802","https://openalex.org/W2087874897","https://openalex.org/W2090469542","https://openalex.org/W2108704847","https://openalex.org/W2117740782","https://openalex.org/W2146531915","https://openalex.org/W2147856686","https://openalex.org/W3009721660","https://openalex.org/W4206805073","https://openalex.org/W4294967943"],"related_works":["https://openalex.org/W2895616265","https://openalex.org/W2349517432","https://openalex.org/W2026098892","https://openalex.org/W3212487472","https://openalex.org/W2148887744","https://openalex.org/W4298221493","https://openalex.org/W2362545535","https://openalex.org/W2052027214","https://openalex.org/W4302277231","https://openalex.org/W2621644573"],"abstract_inverted_index":{"We":[0],"establish":[1],"the":[2,5,18,27,41,46,71,88],"relation":[3],"between":[4],"extended":[6],"(i.e.":[7],"I":[8],"=":[9],"\u221e)":[10],"one-dimensional":[11],"binary":[12],"Cellular":[13],"Automata":[14],"(1D":[15],"CA)":[16],"and":[17,51,82],"bi-infinite":[19],"symbolic":[20,23,42],"sequences":[21],"in":[22,40,77,87],"dynamics.":[24],"That":[25],"is,":[26],"256":[28,36,66],"local":[29,37,67],"rules":[30],"of":[31],"1D":[32],"CA":[33],"correspond":[34],"to":[35],"rule":[38,68],"mappings":[39,69,86],"space.":[43],"By":[44],"employing":[45],"two":[47],"homeomorphisms":[48],"T":[49],"\u2020":[50],"[Formula:":[52],"see":[53],"text]":[54],"from":[55],"[Chua":[56,78],"et":[57,79],"al.,":[58,80],"2004]":[59,81],"for":[60],"finite":[61],"I,":[62],"we":[63],"classify":[64],"these":[65],"into":[70],"same":[72,89],"88":[73],"equivalence":[74,90],"classes":[75],"identified":[76],"[Chua,":[83],"2006].":[84],"Different":[85],"class":[91],"are":[92],"mutually":[93],"topologically":[94],"conjugate.":[95]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}