{"id":"https://openalex.org/W4239246705","doi":"https://doi.org/10.1016/s0166-218x(96)00050-9","title":"VC-dimensions of finite automata and commutative finite automata with k letters and n states","display_name":"VC-dimensions of finite automata and commutative finite automata with k letters and n states","publication_year":1997,"publication_date":"1997-05-01","ids":{"openalex":"https://openalex.org/W4239246705","doi":"https://doi.org/10.1016/s0166-218x(96)00050-9"},"language":"en","primary_location":{"id":"doi:10.1016/s0166-218x(96)00050-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0166-218x(96)00050-9","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Applied Mathematics","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/A5012160957","display_name":"Yoshiyasu Ishigami","orcid":null},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yoshiyasu Ishigami","raw_affiliation_strings":["Department of Computer Science and Information Mathematics, The University of Electro-Communications, Chofugaoka, Chofu City, Tokyo, 182 Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Information Mathematics, The University of Electro-Communications, Chofugaoka, Chofu City, Tokyo, 182 Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046203712","display_name":"Seiichi Tani","orcid":"https://orcid.org/0000-0001-7773-3585"},"institutions":[{"id":"https://openalex.org/I1314466530","display_name":"Tokai University","ror":"https://ror.org/01p7qe739","country_code":"JP","type":"education","lineage":["https://openalex.org/I1314466530"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Sei'ichi Tani","raw_affiliation_strings":["Department of Mathematics, Tokai University, Kitakaname, Hiratsuka City, Kanagawa, 259-12 Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tokai University, Kitakaname, Hiratsuka City, Kanagawa, 259-12 Japan","institution_ids":["https://openalex.org/I1314466530"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2750,"currency":"USD","value_usd":2750},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.36765659,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"74","issue":"3","first_page":"229","last_page":"240"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9995999932289124,"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":0.9865000247955322,"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/mathematics","display_name":"Mathematics","score":0.8033299446105957},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.7839188575744629},{"id":"https://openalex.org/keywords/quantum-finite-automata","display_name":"Quantum finite automata","score":0.6849873661994934},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.6758397817611694},{"id":"https://openalex.org/keywords/deterministic-finite-automaton","display_name":"Deterministic finite automaton","score":0.630752682685852},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.6235722899436951},{"id":"https://openalex.org/keywords/dfa-minimization","display_name":"DFA minimization","score":0.5361533164978027},{"id":"https://openalex.org/keywords/\u03c9-automaton","display_name":"\u03c9-automaton","score":0.4676615297794342},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4507076144218445},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41983562707901},{"id":"https://openalex.org/keywords/nondeterministic-finite-automaton","display_name":"Nondeterministic finite automaton","score":0.4190562665462494},{"id":"https://openalex.org/keywords/automata-theory","display_name":"Automata theory","score":0.38333895802497864},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32980263233184814},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31244128942489624},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.16902750730514526},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16478943824768066},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09994959831237793}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8033299446105957},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.7839188575744629},{"id":"https://openalex.org/C174327141","wikidata":"https://www.wikidata.org/wiki/Q176837","display_name":"Quantum finite automata","level":4,"score":0.6849873661994934},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.6758397817611694},{"id":"https://openalex.org/C104091681","wikidata":"https://www.wikidata.org/wiki/Q837528","display_name":"Deterministic finite automaton","level":3,"score":0.630752682685852},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.6235722899436951},{"id":"https://openalex.org/C65753522","wikidata":"https://www.wikidata.org/wiki/Q5204896","display_name":"DFA minimization","level":5,"score":0.5361533164978027},{"id":"https://openalex.org/C92710233","wikidata":"https://www.wikidata.org/wiki/Q291256","display_name":"\u03c9-automaton","level":5,"score":0.4676615297794342},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4507076144218445},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41983562707901},{"id":"https://openalex.org/C158008952","wikidata":"https://www.wikidata.org/wiki/Q617295","display_name":"Nondeterministic finite automaton","level":4,"score":0.4190562665462494},{"id":"https://openalex.org/C116248031","wikidata":"https://www.wikidata.org/wiki/Q214526","display_name":"Automata theory","level":3,"score":0.38333895802497864},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32980263233184814},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31244128942489624},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.16902750730514526},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16478943824768066},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09994959831237793}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0166-218x(96)00050-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0166-218x(96)00050-9","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320912","display_name":"Ministry of Education, Culture, Sports, Science and Technology","ror":"https://ror.org/048rj2z13"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1989445634","https://openalex.org/W2010138282","https://openalex.org/W2053605285","https://openalex.org/W2067220985","https://openalex.org/W2154952480","https://openalex.org/W2913222977","https://openalex.org/W4238284510","https://openalex.org/W4252861488","https://openalex.org/W4256175731","https://openalex.org/W4302339081","https://openalex.org/W6650982137","https://openalex.org/W6678613396","https://openalex.org/W6759106645"],"related_works":["https://openalex.org/W1975910189","https://openalex.org/W4205935260","https://openalex.org/W2030569822","https://openalex.org/W2537940722","https://openalex.org/W2368684504","https://openalex.org/W2079577017","https://openalex.org/W2032001066","https://openalex.org/W2000290048","https://openalex.org/W3143588635","https://openalex.org/W2160879187"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
