{"id":"https://openalex.org/W2579020504","doi":"https://doi.org/10.1007/978-3-319-60252-3_7","title":"Most Complex Non-returning Regular Languages","display_name":"Most Complex Non-returning Regular Languages","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2579020504","doi":"https://doi.org/10.1007/978-3-319-60252-3_7","mag":"2579020504"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-60252-3_7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-60252-3_7","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://inria.hal.science/hal-01656998","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016883956","display_name":"Janusz Brzozowski","orcid":"https://orcid.org/0000-0003-3390-2767"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Janusz A. Brzozowski","raw_affiliation_strings":["David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada"],"affiliations":[{"raw_affiliation_string":"David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050424365","display_name":"Sylvie Davies","orcid":"https://orcid.org/0000-0002-5010-4831"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Sylvie Davies","raw_affiliation_strings":["Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5016883956"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":1.0682,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.7316888,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"89","last_page":"101"},"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":0.9955000281333923,"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/T10911","display_name":"Chemical Synthesis and Analysis","score":0.9908000230789185,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6618069410324097},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.6576790809631348},{"id":"https://openalex.org/keywords/concatenation","display_name":"Concatenation (mathematics)","score":0.6574548482894897},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5765948295593262},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.5564157962799072},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5220950841903687},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5107762813568115},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5079286694526672},{"id":"https://openalex.org/keywords/star","display_name":"Star (game theory)","score":0.5062291026115417},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4948529601097107},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.4245024025440216},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.41509634256362915},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3904613256454468},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2737516760826111},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.24951815605163574},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.22355961799621582}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6618069410324097},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.6576790809631348},{"id":"https://openalex.org/C87619178","wikidata":"https://www.wikidata.org/wiki/Q126002","display_name":"Concatenation (mathematics)","level":2,"score":0.6574548482894897},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5765948295593262},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.5564157962799072},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5220950841903687},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5107762813568115},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5079286694526672},{"id":"https://openalex.org/C2780897414","wikidata":"https://www.wikidata.org/wiki/Q7600592","display_name":"Star (game theory)","level":2,"score":0.5062291026115417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4948529601097107},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.4245024025440216},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.41509634256362915},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3904613256454468},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2737516760826111},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.24951815605163574},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.22355961799621582},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-319-60252-3_7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-60252-3_7","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:HAL:hal-01656998v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01656998","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"19th International Conference on Descriptional Complexity of Formal Systems (DCFS), Jul 2017, Milano, Italy. pp.89-101, ⟨10.1007/978-3-319-60252-3_7⟩","raw_type":"Conference papers"},{"id":"pmh:oai:uwspace.uwaterloo.ca:10012/13157","is_oa":false,"landing_page_url":"http://hdl.handle.net/10012/13157","pdf_url":null,"source":{"id":"https://openalex.org/S4306401661","display_name":"UWSpace (University of Waterloo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I151746483","host_organization_name":"University of Waterloo","host_organization_lineage":["https://openalex.org/I151746483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference Paper"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01656998v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01656998","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"19th International Conference on Descriptional Complexity of Formal Systems (DCFS), Jul 2017, Milano, Italy. pp.89-101, ⟨10.1007/978-3-319-60252-3_7⟩","raw_type":"Conference papers"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.5,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1492009014","https://openalex.org/W1495359240","https://openalex.org/W1524205571","https://openalex.org/W1768118166","https://openalex.org/W1975431188","https://openalex.org/W2022378152","https://openalex.org/W2132750992","https://openalex.org/W2143586833","https://openalex.org/W2153026689","https://openalex.org/W2430843852","https://openalex.org/W2786516640","https://openalex.org/W2912226968","https://openalex.org/W2913344232","https://openalex.org/W2913383557","https://openalex.org/W3103352697","https://openalex.org/W4210981569","https://openalex.org/W4211010176"],"related_works":["https://openalex.org/W203356024","https://openalex.org/W1972592804","https://openalex.org/W2510632068","https://openalex.org/W252108735","https://openalex.org/W2063737596","https://openalex.org/W1607287758","https://openalex.org/W2240836793","https://openalex.org/W1540583425","https://openalex.org/W2064508306","https://openalex.org/W2061007349"],"abstract_inverted_index":{"A":[0],"regular":[1],"language":[2,157,191],"L":[3],"is":[4],"non-returning":[5,156,179,190],"if":[6],"in":[7],"the":[8,20,31,94,111,120,135,150,172,194],"minimal":[9],"deterministic":[10],"finite":[11],"automaton":[12],"accepting":[13],"it":[14],"there":[15,83,185],"are":[16,45,104],"no":[17],"transitions":[18],"into":[19],"initial":[21],"state.":[22],"Eom,":[23],"Han":[24],"and":[25,37,40,58,98,125,161],"Jir\u00e1skov\u00e1":[26],"derived":[27,53],"upper":[28,54,132],"bounds":[29,44,55,121,133,195],"on":[30,134],"state":[32,89,136,174],"complexity":[33,90,137,199],"of":[34,71,88,113,138,154,176,178],"boolean":[35,126],"operations":[36,140],"Kleene":[38],"star,":[39,124],"proved":[41],"that":[42,77,92,99,141,149,184,192],"these":[43,198],"tight":[46,131],"using":[47,60],"two":[48],"different":[49,62,73,145],"binary":[50,117,139],"witnesses.":[51,64],"They":[52],"for":[56,78,96,122,196],"concatenation":[57],"reversal":[59,97],"three":[61,102],"ternary":[63,86],"These":[65],"five":[66],"witnesses":[67],"use":[68],"a":[69,85,155,187],"total":[70],"six":[72],"transformations.":[74],"We":[75,128,147,170],"show":[76,183],"each":[79],"$$n":[80],"\\geqslant":[81],"4$$":[82],"exists":[84,186],"witness":[87,115],"n":[91],"meets":[93,193],"bound":[95],"at":[100,163],"least":[101,164],"letters":[103],"needed":[105],"to":[106,116],"meet":[107,119],"this":[108,114],"bound.":[109],"Moreover,":[110],"restrictions":[112],"alphabets":[118],"product,":[123],"operations.":[127],"also":[129],"derive":[130],"take":[142],"arguments":[143],"with":[144],"alphabets.":[146],"prove":[148],"maximal":[151,173],"syntactic":[152],"semigroup":[153],"has":[158],"$$(n-1)^n$$":[159],"elements":[160],"requires":[162],"$$\\left(":[165],"{\\begin{array}{c}n\\\\":[166],"2\\end{array}}\\right)":[167],"$$":[168],"generators.":[169],"find":[171],"complexities":[175],"atoms":[177],"languages.":[180],"Finally,":[181],"we":[182],"most":[188],"complex":[189],"all":[197],"measures.":[200]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}