{"id":"https://openalex.org/W1523718026","doi":"https://doi.org/10.1017/s0960129508007342","title":"Unary automatic graphs: an algorithmic perspective","display_name":"Unary automatic graphs: an algorithmic perspective","publication_year":2009,"publication_date":"2009-02-01","ids":{"openalex":"https://openalex.org/W1523718026","doi":"https://doi.org/10.1017/s0960129508007342","mag":"1523718026"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129508007342","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129508007342","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://openrepository.aut.ac.nz/bitstreams/9b544e75-5b47-46b6-896a-276936a14b9c/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109808768","display_name":"Bakhadyr Khoussainov","orcid":null},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"BAKHADYR KHOUSSAINOV","raw_affiliation_strings":["Department of Computer Science, University of Auckland, Auckland, New Zealand Emails:","Department of Computer Science, University of Auckland, Auckland, New Zealand Emails: bmk@cs.auckland.ac.nz; jliu036@aucklanduni.ac.nz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Auckland, Auckland, New Zealand Emails:","institution_ids":["https://openalex.org/I154130895"]},{"raw_affiliation_string":"Department of Computer Science, University of Auckland, Auckland, New Zealand Emails: bmk@cs.auckland.ac.nz; jliu036@aucklanduni.ac.nz","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083914998","display_name":"Jiamou Liu","orcid":"https://orcid.org/0000-0002-0824-0899"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"JIAMOU LIU","raw_affiliation_strings":["Department of Computer Science, University of Auckland, Auckland, New Zealand Emails:","Department of Computer Science, University of Auckland, Auckland, New Zealand Emails: bmk@cs.auckland.ac.nz; jliu036@aucklanduni.ac.nz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Auckland, Auckland, New Zealand Emails:","institution_ids":["https://openalex.org/I154130895"]},{"raw_affiliation_string":"Department of Computer Science, University of Auckland, Auckland, New Zealand Emails: bmk@cs.auckland.ac.nz; jliu036@aucklanduni.ac.nz","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026955369","display_name":"Mia Minnes","orcid":"https://orcid.org/0000-0001-6601-0875"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"MIA MINNES","raw_affiliation_strings":["Department of Mathematics, Cornell University, Ithaca, NY, USA Email:","Department of mathematics, cornell university, ithaca, ny, usa email: minnes@math.mit.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cornell University, Ithaca, NY, USA Email:","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Department of mathematics, cornell university, ithaca, ny, usa email: minnes@math.mit.edu#TAB#","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3472,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.58009651,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"19","issue":"1","first_page":"133","last_page":"152"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","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/T11567","display_name":"semigroups and automata theory","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/T11727","display_name":"Advanced Algebra and Logic","score":0.9975000023841858,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/unary-operation","display_name":"Unary operation","score":0.8619444370269775},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5005404949188232},{"id":"https://openalex.org/keywords/deterministic-finite-automaton","display_name":"Deterministic finite automaton","score":0.4823119640350342},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4591521620750427},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.45095646381378174},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.4422680735588074},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.4299662113189697},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4299173355102539},{"id":"https://openalex.org/keywords/cograph","display_name":"Cograph","score":0.4140980541706085},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.4119972884654999},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.40862607955932617},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.4032549560070038},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38410595059394836},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.3806220293045044},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.30666330456733704},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27538830041885376},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.16321256756782532}],"concepts":[{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.8619444370269775},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5005404949188232},{"id":"https://openalex.org/C104091681","wikidata":"https://www.wikidata.org/wiki/Q837528","display_name":"Deterministic finite automaton","level":3,"score":0.4823119640350342},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4591521620750427},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.45095646381378174},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.4422680735588074},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.4299662113189697},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4299173355102539},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.4140980541706085},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.4119972884654999},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.40862607955932617},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.4032549560070038},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38410595059394836},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.3806220293045044},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.30666330456733704},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27538830041885376},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.16321256756782532},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1017/s0960129508007342","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129508007342","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:openrepository.aut.ac.nz:10292/2817","is_oa":true,"landing_page_url":"https://hdl.handle.net/10292/2817","pdf_url":"https://openrepository.aut.ac.nz/bitstreams/9b544e75-5b47-46b6-896a-276936a14b9c/download","source":{"id":"https://openalex.org/S4306401809","display_name":"Tuwhera (Auckland University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39854758","host_organization_name":"Auckland University of Technology","host_organization_lineage":["https://openalex.org/I39854758"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.121.1873","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.121.1873","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.auckland.ac.nz/~jliu036/fullpaper.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.311.941","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.311.941","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0809.3330v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.85.6849","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.85.6849","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cornell.edu/~minnes/unary.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.913.7259","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.913.7259","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://aut.researchgateway.ac.nz/bitstream/handle/10292/2812/tamc08.pdf%3Bjsessionid%3D48EC114DF8731D3D26EDA4CC5B78754A?sequence%3D2","raw_type":"text"},{"id":"pmh:oai:aut.researchgateway.ac.nz:10292/2817","is_oa":false,"landing_page_url":"http://hdl.handle.net/10292/2817","pdf_url":null,"source":{"id":"https://openalex.org/S4406922880","display_name":"AUT Scholarly Commons","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:openrepository.aut.ac.nz:10292/2817","is_oa":true,"landing_page_url":"https://hdl.handle.net/10292/2817","pdf_url":"https://openrepository.aut.ac.nz/bitstreams/9b544e75-5b47-46b6-896a-276936a14b9c/download","source":{"id":"https://openalex.org/S4306401809","display_name":"Tuwhera (Auckland University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39854758","host_organization_name":"Auckland University of Technology","host_organization_lineage":["https://openalex.org/I39854758"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1523718026.pdf","grobid_xml":"https://content.openalex.org/works/W1523718026.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W37260162","https://openalex.org/W51516856","https://openalex.org/W655258421","https://openalex.org/W1489366126","https://openalex.org/W1491036809","https://openalex.org/W1501737527","https://openalex.org/W1517606395","https://openalex.org/W1547822735","https://openalex.org/W1585989904","https://openalex.org/W1586329108","https://openalex.org/W1589224558","https://openalex.org/W1966217515","https://openalex.org/W2033186040","https://openalex.org/W2101592234","https://openalex.org/W2109287809","https://openalex.org/W2138856440","https://openalex.org/W2162583406","https://openalex.org/W2296095876","https://openalex.org/W4230164765","https://openalex.org/W4236241665","https://openalex.org/W4240244556","https://openalex.org/W6601537402","https://openalex.org/W6634961419","https://openalex.org/W6641740895"],"related_works":["https://openalex.org/W2031276298","https://openalex.org/W4220852510","https://openalex.org/W2061237693","https://openalex.org/W3130332934","https://openalex.org/W2169699292","https://openalex.org/W110470963","https://openalex.org/W1977862280","https://openalex.org/W2083238533","https://openalex.org/W1971319751","https://openalex.org/W1919313975"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"infinite":[3,66],"graphs":[4,50],"produced":[5,16],"from":[6,77],"a":[7,60,96,125],"natural":[8],"unfolding":[9],"operation":[10],"applied":[11],"to":[12,64],"finite":[13,22,37,53],"graphs.":[14],"Graphs":[15],"using":[17,116],"such":[18,48],"operations":[19],"are":[20,75],"of":[21,47,92],"degree":[23],"and":[24,80,110],"automatic":[25],"over":[26,39],"the":[27,40,73,82,100,103,111,121],"unary":[28,41],"alphabet":[29],"(that":[30],"is,":[31],"they":[32],"can":[33],"be":[34],"described":[35],"by":[36],"automata":[38],"alphabet).":[42],"We":[43,86],"investigate":[44],"algorithmic":[45],"properties":[46],"unfolded":[49],"given":[51,61,70],"their":[52],"presentations.":[54],"In":[55],"particular,":[56],"we":[57,129],"ask":[58],"whether":[59,68,81],"node":[62],"belongs":[63],"an":[65,117],"component,":[67],"two":[69],"nodes":[71],"in":[72,107,124,134],"graph":[74,83],"reachable":[76],"one":[78],"another":[79],"is":[84,106,114],"connected.":[85],"give":[87],"polynomial-time":[88],"algorithms":[89,139],"for":[90,102],"each":[91],"these":[93],"questions.":[94],"For":[95],"fixed":[97],"input":[98],"graph,":[99],"algorithm":[101],"first":[104],"question":[105,113],"constant":[108],"time":[109],"second":[112],"decided":[115],"automaton":[118],"that":[119],"recognises":[120],"reachability":[122],"relation":[123],"uniform":[126],"way.":[127],"Hence,":[128],"improve":[130],"on":[131],"previous":[132],"work,":[133],"which":[135],"non-elementary":[136],"or":[137],"non-uniform":[138],"were":[140],"found.":[141]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}