{"id":"https://openalex.org/W2772918710","doi":"https://doi.org/10.1142/s0129054117400044","title":"The Degree of Irreversibility in Deterministic Finite Automata","display_name":"The Degree of Irreversibility in Deterministic Finite Automata","publication_year":2017,"publication_date":"2017-08-01","ids":{"openalex":"https://openalex.org/W2772918710","doi":"https://doi.org/10.1142/s0129054117400044","mag":"2772918710"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054117400044","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054117400044","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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 Foundations of Computer Science","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/A5038693222","display_name":"Holger Bock Axelsen","orcid":"https://orcid.org/0000-0002-0034-2874"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Holger Bock Axelsen","raw_affiliation_strings":["Department of Computer Science, University of Copenhagen, Universitetsparken 5, Copenhagen, Denmark"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Copenhagen, Universitetsparken 5, Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016664760","display_name":"Markus Holzer","orcid":"https://orcid.org/0000-0003-4224-4014"},"institutions":[{"id":"https://openalex.org/I200763008","display_name":"University of Giessen","ror":"https://ror.org/033eqas34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200763008"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Markus Holzer","raw_affiliation_strings":["Institut f\u00fcr Informatik, Universit\u00e4t Giessen, Arndtstrasse\u00a02, 35392 Giessen, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, Universit\u00e4t Giessen, Arndtstrasse\u00a02, 35392 Giessen, Germany","institution_ids":["https://openalex.org/I200763008"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026803820","display_name":"Martin Kutrib","orcid":"https://orcid.org/0000-0002-9564-2625"},"institutions":[{"id":"https://openalex.org/I200763008","display_name":"University of Giessen","ror":"https://ror.org/033eqas34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200763008"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Kutrib","raw_affiliation_strings":["Institut f\u00fcr Informatik, Universit\u00e4t Giessen, Arndtstrasse\u00a02, 35392 Giessen, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, Universit\u00e4t Giessen, Arndtstrasse\u00a02, 35392 Giessen, Germany","institution_ids":["https://openalex.org/I200763008"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038693222"],"corresponding_institution_ids":["https://openalex.org/I124055696"],"apc_list":null,"apc_paid":null,"fwci":0.4729,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.68674035,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"28","issue":"05","first_page":"503","last_page":"522"},"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/T12029","display_name":"DNA and Biological Computing","score":0.9991000294685364,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.996399998664856,"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/deterministic-finite-automaton","display_name":"Deterministic finite automaton","score":0.8320479989051819},{"id":"https://openalex.org/keywords/nondeterministic-finite-automaton","display_name":"Nondeterministic finite automaton","score":0.8318133354187012},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.7090983986854553},{"id":"https://openalex.org/keywords/deterministic-automaton","display_name":"Deterministic automaton","score":0.7087326049804688},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.7058396935462952},{"id":"https://openalex.org/keywords/concatenation","display_name":"Concatenation (mathematics)","score":0.689312756061554},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.610071063041687},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5581369400024414},{"id":"https://openalex.org/keywords/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.5419275760650635},{"id":"https://openalex.org/keywords/dfa-minimization","display_name":"DFA minimization","score":0.5131621956825256},{"id":"https://openalex.org/keywords/quantum-finite-automata","display_name":"Quantum finite automata","score":0.5112917423248291},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.5066131353378296},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5031463503837585},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45146939158439636},{"id":"https://openalex.org/keywords/\u03c9-automaton","display_name":"\u03c9-automaton","score":0.4167507588863373},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.33044102787971497},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.24947229027748108},{"id":"https://openalex.org/keywords/automata-theory","display_name":"Automata theory","score":0.24610915780067444},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24245306849479675},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22427672147750854},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.1753171980381012}],"concepts":[{"id":"https://openalex.org/C104091681","wikidata":"https://www.wikidata.org/wiki/Q837528","display_name":"Deterministic finite automaton","level":3,"score":0.8320479989051819},{"id":"https://openalex.org/C158008952","wikidata":"https://www.wikidata.org/wiki/Q617295","display_name":"Nondeterministic finite automaton","level":4,"score":0.8318133354187012},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7090983986854553},{"id":"https://openalex.org/C194525867","wikidata":"https://www.wikidata.org/wiki/Q5265707","display_name":"Deterministic automaton","level":3,"score":0.7087326049804688},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.7058396935462952},{"id":"https://openalex.org/C87619178","wikidata":"https://www.wikidata.org/wiki/Q126002","display_name":"Concatenation (mathematics)","level":2,"score":0.689312756061554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.610071063041687},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5581369400024414},{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.5419275760650635},{"id":"https://openalex.org/C65753522","wikidata":"https://www.wikidata.org/wiki/Q5204896","display_name":"DFA minimization","level":5,"score":0.5131621956825256},{"id":"https://openalex.org/C174327141","wikidata":"https://www.wikidata.org/wiki/Q176837","display_name":"Quantum finite automata","level":4,"score":0.5112917423248291},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.5066131353378296},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5031463503837585},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45146939158439636},{"id":"https://openalex.org/C92710233","wikidata":"https://www.wikidata.org/wiki/Q291256","display_name":"\u03c9-automaton","level":5,"score":0.4167507588863373},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.33044102787971497},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.24947229027748108},{"id":"https://openalex.org/C116248031","wikidata":"https://www.wikidata.org/wiki/Q214526","display_name":"Automata theory","level":3,"score":0.24610915780067444},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24245306849479675},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22427672147750854},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.1753171980381012},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0129054117400044","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054117400044","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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 Foundations of Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/9fc8bd43-f408-4099-8c73-8b920db88c6c","is_oa":false,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/9fc8bd43-f408-4099-8c73-8b920db88c6c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axelsen , H B , Holzer , M & Kutrib , M 2017 , ' The degree of irreversibility in deterministic finite automata ' , International Journal of Foundations of Computer Science , vol. 28 , no. 5 , pp. 503-522 . https://doi.org/10.1142/S0129054117400044","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1998896169","https://openalex.org/W2006629323","https://openalex.org/W2077450865","https://openalex.org/W4233798822","https://openalex.org/W4301662502"],"related_works":["https://openalex.org/W3143588635","https://openalex.org/W2030569822","https://openalex.org/W4205935260","https://openalex.org/W1975910189","https://openalex.org/W2079577017","https://openalex.org/W2537940722","https://openalex.org/W2368684504","https://openalex.org/W2160879187","https://openalex.org/W2000290048","https://openalex.org/W2100711766"],"abstract_inverted_index":{"Recently,":[0],"a":[1,14,62,73,96],"method":[2,51],"to":[3],"decide":[4],"the":[5,10,38,56,68,76,88,93,106,112,129],"NL-complete":[6],"problem":[7,40],"of":[8,70,79,100,108],"whether":[9],"language":[11,101,114],"accepted":[12,23],"by":[13,24,54],"given":[15],"deterministic":[16,27],"finite":[17,28,43],"automaton":[18,29],"(DFA)":[19],"can":[20],"also":[21],"be":[22],"some":[25],"reversible":[26],"(REV-DFA)":[30],"has":[31],"been":[32],"derived.":[33],"Here,":[34],"we":[35],"show":[36,91],"that":[37,92],"corresponding":[39],"for":[41,61,72],"nondeterministic":[42],"automata":[44],"(NFA)":[45],"is":[46],"PSPACE-complete.":[47],"The":[48],"recent":[49],"DFA":[50,57,86],"essentially":[52],"works":[53],"minimizing":[55],"and":[58,90,120],"inspecting":[59],"it":[60],"forbidden":[63,81],"pattern.":[64],"We":[65,103],"here":[66],"study":[67],"degree":[69,94,107],"irreversibility":[71,109],"regular":[74],"language,":[75,89],"minimal":[77],"number":[78],"such":[80],"patterns":[82],"necessary":[83],"in":[84],"any":[85],"accepting":[87],"induces":[95],"strict":[97],"infinite":[98],"hierarchy":[99],"families.":[102],"examine":[104],"how":[105],"behaves":[110],"under":[111],"usual":[113],"operations":[115],"union,":[116],"intersection,":[117],"complement,":[118],"concatenation,":[119],"Kleene":[121],"star,":[122],"showing":[123],"tight":[124],"bounds":[125],"(some":[126],"asymptotically)":[127],"on":[128],"degree.":[130]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-03-16T09:10:04.655348","created_date":"2025-10-10T00:00:00"}
