{"id":"https://openalex.org/W1816155648","doi":"https://doi.org/10.3233/fi-2011-540","title":"State Complexity of Union and Intersection for Two-way Nondeterministic Finite Automata","display_name":"State Complexity of Union and Intersection for Two-way Nondeterministic Finite Automata","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1816155648","doi":"https://doi.org/10.3233/fi-2011-540","mag":"1816155648"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2011-540","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2011-540","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","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/A5009330299","display_name":"Michal Kunc","orcid":null},"institutions":[{"id":"https://openalex.org/I21449261","display_name":"Masaryk University","ror":"https://ror.org/02j46qs45","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21449261"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Michal Kunc","raw_affiliation_strings":["Department of Mathematics, Masaryk University, Brno, Czech Republic. kunc@math.muni.cz","(Correspd.) (Supported by grant 201/09/1313 of the Grant Agency of the Czech Republic) Department of Mathematics, Masaryk University, Brno, Czech Republic. kunc@math.muni.cz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Masaryk University, Brno, Czech Republic. kunc@math.muni.cz","institution_ids":["https://openalex.org/I21449261"]},{"raw_affiliation_string":"(Correspd.) (Supported by grant 201/09/1313 of the Grant Agency of the Czech Republic) Department of Mathematics, Masaryk University, Brno, Czech Republic. kunc@math.muni.cz","institution_ids":["https://openalex.org/I21449261"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005683089","display_name":"Alexander Okhotin","orcid":"https://orcid.org/0000-0002-1615-2725"},"institutions":[{"id":"https://openalex.org/I155660961","display_name":"University of Turku","ror":"https://ror.org/05vghhr25","country_code":"FI","type":"education","lineage":["https://openalex.org/I155660961"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Alexander Okhotin","raw_affiliation_strings":["Department of Mathematics, University of Turku, Turku, FI\u201320014, Finland. alexander.okhotin@utu.fi","(Additional affiliation: Academy of Finland. Supported by the Academy of Finland under grant 134860) Department of Mathematics, University of Turku, Turku, FI-20014, Finland. alexander.okhotin@utu ...#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Turku, Turku, FI\u201320014, Finland. alexander.okhotin@utu.fi","institution_ids":["https://openalex.org/I155660961"]},{"raw_affiliation_string":"(Additional affiliation: Academy of Finland. Supported by the Academy of Finland under grant 134860) Department of Mathematics, University of Turku, Turku, FI-20014, Finland. alexander.okhotin@utu ...#TAB#","institution_ids":["https://openalex.org/I155660961"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009330299"],"corresponding_institution_ids":["https://openalex.org/I21449261"],"apc_list":null,"apc_paid":null,"fwci":0.3261,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.57550348,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"110","issue":"1-4","first_page":"231","last_page":"239"},"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":0.996399998664856,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9947999715805054,"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/intersection","display_name":"Intersection (aeronautics)","score":0.7574980854988098},{"id":"https://openalex.org/keywords/nondeterministic-finite-automaton","display_name":"Nondeterministic finite automaton","score":0.7501150369644165},{"id":"https://openalex.org/keywords/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.6768109798431396},{"id":"https://openalex.org/keywords/deterministic-finite-automaton","display_name":"Deterministic finite automaton","score":0.5698727369308472},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.541091799736023},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.4676954746246338},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4604725241661072},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43141061067581177},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42951372265815735},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.37337881326675415},{"id":"https://openalex.org/keywords/automata-theory","display_name":"Automata theory","score":0.3143649697303772},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1690073311328888},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.05147719383239746}],"concepts":[{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.7574980854988098},{"id":"https://openalex.org/C158008952","wikidata":"https://www.wikidata.org/wiki/Q617295","display_name":"Nondeterministic finite automaton","level":4,"score":0.7501150369644165},{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.6768109798431396},{"id":"https://openalex.org/C104091681","wikidata":"https://www.wikidata.org/wiki/Q837528","display_name":"Deterministic finite automaton","level":3,"score":0.5698727369308472},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.541091799736023},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.4676954746246338},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4604725241661072},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43141061067581177},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42951372265815735},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37337881326675415},{"id":"https://openalex.org/C116248031","wikidata":"https://www.wikidata.org/wiki/Q214526","display_name":"Automata theory","level":3,"score":0.3143649697303772},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1690073311328888},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.05147719383239746},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/fi-2011-540","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2011-540","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W15905929","https://openalex.org/W23998349","https://openalex.org/W1500042303","https://openalex.org/W1510604108","https://openalex.org/W1649246749","https://openalex.org/W1662891443","https://openalex.org/W1971747251","https://openalex.org/W1975246937","https://openalex.org/W1977193848","https://openalex.org/W1978405212","https://openalex.org/W1981823970","https://openalex.org/W1989657066","https://openalex.org/W2001082538","https://openalex.org/W2006629323","https://openalex.org/W2011252827","https://openalex.org/W2034243894","https://openalex.org/W2040161039","https://openalex.org/W2054801208","https://openalex.org/W2082934005","https://openalex.org/W2095282951","https://openalex.org/W2149288970","https://openalex.org/W2285266141"],"related_works":["https://openalex.org/W2111868903","https://openalex.org/W1428391281","https://openalex.org/W2100711766","https://openalex.org/W2059979350","https://openalex.org/W3087272834","https://openalex.org/W1982464584","https://openalex.org/W4205935260","https://openalex.org/W2146605784","https://openalex.org/W4281261571","https://openalex.org/W2066562587"],"abstract_inverted_index":{"The":[0,48,59],"number":[1,42],"of":[2,15,43,62,135,146,162],"states":[3,44],"in":[4],"a":[5,56,156],"two-way":[6],"nondeterministic":[7],"finite":[8],"automaton":[9],"(2NFA)":[10],"needed":[11],"to":[12,28],"represent":[13],"intersection":[14],"languages":[16,54],"given":[17],"by":[18],"an":[19,23,141],"m-state":[20],"2NFA":[21,25],"and":[22,33,99],"n-state":[24],"is":[26,45,51,65,166],"shown":[27],"be":[29],"at":[30,34],"least":[31],"m+n":[32],"most":[35],"m+n+1.":[36],"For":[37,139],"the":[38,41,63,66],"union":[39],"operation,":[40],"exactly":[46],"m+n.":[47],"lower":[49],"bound":[50],"established":[52,167],"for":[53,70],"over":[55],"one-letter":[57],"alphabet.":[58],"key":[60],"point":[61],"argument":[64],"following":[67],"number-theoretic":[68],"lemma:":[69],"all":[71,110],"m,":[72,77,150],"n":[73,78,100,151],"\u2265":[74,131],"2":[75,132],"with":[76,82],"\u2260":[79],"6":[80],"(and":[81],"finitely":[83],"many":[84],"other":[85],"exceptions),":[86],"there":[87],"exist":[88],"partitions":[89,145],"m":[90],"=":[91,101],"p":[92,97,112,119],"1":[93,103,113,123],"+.":[94,104],".":[95,105,115,116,117,125,126,127],".+":[96],"k":[98,120],"q":[102,122,129],".+q":[106],"l":[107,130],",":[108,114,118,121,124,128],"where":[109],"numbers":[111,149],"are":[133],"powers":[134],"pairwise":[136,163],"distinct":[137,164],"primes.":[138],"completeness,":[140],"analogous":[142],"statement":[143],"about":[144],"any":[147],"two":[148],"\u2209":[152],"{4,":[153],"6}":[154],"(with":[155],"few":[157],"more":[158],"exceptions)":[159],"into":[160],"sums":[161],"primes":[165],"as":[168],"well.":[169]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-02T06:04:40.494371","created_date":"2025-10-10T00:00:00"}
