{"id":"https://openalex.org/W2025689196","doi":"https://doi.org/10.1142/s0129054105003352","title":"NON-UNIQUENESS AND RADIUS OF CYCLIC UNARY NFAs","display_name":"NON-UNIQUENESS AND RADIUS OF CYCLIC UNARY NFAs","publication_year":2005,"publication_date":"2005-10-01","ids":{"openalex":"https://openalex.org/W2025689196","doi":"https://doi.org/10.1142/s0129054105003352","mag":"2025689196"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054105003352","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054105003352","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/A5002321933","display_name":"Michael Domaratzki","orcid":"https://orcid.org/0000-0001-9129-6676"},"institutions":[{"id":"https://openalex.org/I92688161","display_name":"Acadia University","ror":"https://ror.org/00839we02","country_code":"CA","type":"education","lineage":["https://openalex.org/I92688161"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"MICHAEL DOMARATZKI","raw_affiliation_strings":["Jodrey School of Computer Science,  Acadia University, Wolfville, NS, B4P 2R6, Canada","Jodrey School of Computer Science, Acadia University, Wolfville, NS, B4P 2R6, Canada"],"affiliations":[{"raw_affiliation_string":"Jodrey School of Computer Science,  Acadia University, Wolfville, NS, B4P 2R6, Canada","institution_ids":["https://openalex.org/I92688161"]},{"raw_affiliation_string":"Jodrey School of Computer Science, Acadia University, Wolfville, NS, B4P 2R6, Canada","institution_ids":["https://openalex.org/I92688161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058555323","display_name":"Keith Ellul","orcid":null},"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":"KEITH ELLUL","raw_affiliation_strings":["School of Computer Science,  University of Waterloo, Waterloo, ON, N2L 3G1, Canada"],"affiliations":[{"raw_affiliation_string":"School of Computer Science,  University of Waterloo, Waterloo, ON, N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113632449","display_name":"JEFFREY SHALLIT","orcid":null},"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":"JEFFREY SHALLIT","raw_affiliation_strings":["School of Computer Science,  University of Waterloo, Waterloo, ON, N2L 3G1, Canada"],"affiliations":[{"raw_affiliation_string":"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/A5100683205","display_name":"Ming\u2010Wei Wang","orcid":"https://orcid.org/0000-0001-6550-9017"},"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":"MING-WEI WANG","raw_affiliation_strings":["School of Computer Science,  University of Waterloo, Waterloo, ON, N2L 3G1, Canada"],"affiliations":[{"raw_affiliation_string":"School of Computer Science,  University of Waterloo, Waterloo, ON, N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5002321933"],"corresponding_institution_ids":["https://openalex.org/I92688161"],"apc_list":null,"apc_paid":null,"fwci":1.0541,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.76174227,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"16","issue":"05","first_page":"883","last_page":"896"},"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/T11269","display_name":"Algorithms and Data Compression","score":0.9901000261306763,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9840999841690063,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.8950637578964233},{"id":"https://openalex.org/keywords/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.7500054836273193},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.7023085951805115},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6670371294021606},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5934675335884094},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.5468834638595581},{"id":"https://openalex.org/keywords/diophantine-equation","display_name":"Diophantine equation","score":0.5445539951324463},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5059108138084412},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41898196935653687},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4162292778491974},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19495657086372375},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09051328897476196},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.07396984100341797},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.058654069900512695},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05759149789810181}],"concepts":[{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.8950637578964233},{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.7500054836273193},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.7023085951805115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6670371294021606},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5934675335884094},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.5468834638595581},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.5445539951324463},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5059108138084412},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41898196935653687},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4162292778491974},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19495657086372375},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09051328897476196},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.07396984100341797},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.058654069900512695},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05759149789810181},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054105003352","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054105003352","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W191942163","https://openalex.org/W1532594152","https://openalex.org/W1564368568","https://openalex.org/W1971747251","https://openalex.org/W1975977496","https://openalex.org/W1979468280","https://openalex.org/W2000732374","https://openalex.org/W2011252827","https://openalex.org/W2015305877","https://openalex.org/W2054230520","https://openalex.org/W2079158241","https://openalex.org/W2979658900","https://openalex.org/W4245613997","https://openalex.org/W4302339081"],"related_works":["https://openalex.org/W1945859206","https://openalex.org/W4210507006","https://openalex.org/W1971747251","https://openalex.org/W22759520","https://openalex.org/W1607287758","https://openalex.org/W2407531803","https://openalex.org/W3022280117","https://openalex.org/W2913032954","https://openalex.org/W3125702482","https://openalex.org/W2560728105"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"study":[4],"some":[5,39],"properties":[6],"of":[7,19,44,53,66,76,84,97],"cyclic":[8,25,55],"unary":[9,26,45,56],"regular":[10,27,57,86],"languages.":[11,46],"We":[12,36,47,72],"find":[13],"a":[14,30,54,74,85],"connection":[15],"between":[16],"the":[17,20,42,50,67,81,94],"uniqueness":[18],"minimal":[21,68,95,99],"NFA":[22],"for":[23,70],"certain":[24],"languages":[28],"and":[29],"Diophantine":[31],"equation":[32],"studied":[33],"by":[34,64,93],"Sylvester.":[35],"also":[37],"obtain":[38],"results":[40],"on":[41],"radius":[43,52,83,96],"show":[48],"that":[49,80],"nondeterministic":[51,82],"language":[58,87],"L":[59],"is":[60],"not":[61],"necessarily":[62,89],"obtained":[63],"any":[65],"NFAs":[69],"L.":[71],"give":[73],"class":[75],"examples":[77],"which":[78],"demonstrates":[79],"cannot":[88],"even":[90],"be":[91],"approximated":[92],"its":[98],"NFAs.":[100]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}