{"id":"https://openalex.org/W1979196995","doi":"https://doi.org/10.1080/00207169708804583","title":"Morphic refinements of nonregular languages","display_name":"Morphic refinements of nonregular languages","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W1979196995","doi":"https://doi.org/10.1080/00207169708804583","mag":"1979196995"},"language":"en","primary_location":{"id":"doi:10.1080/00207169708804583","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169708804583","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer 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/A5010440892","display_name":"John Harrison","orcid":"https://orcid.org/0000-0001-5707-4631"},"institutions":[{"id":"https://openalex.org/I160003610","display_name":"Wilkes University","ror":"https://ror.org/054nntz49","country_code":"US","type":"education","lineage":["https://openalex.org/I160003610"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John Harrison","raw_affiliation_strings":["Department of Mathematics and Computer Science , Wilkes University , Wilkes-Barre, Pa, 18766"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science , Wilkes University , Wilkes-Barre, Pa, 18766","institution_ids":["https://openalex.org/I160003610"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010440892"],"corresponding_institution_ids":["https://openalex.org/I160003610"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10868737,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"3-4","first_page":"181","last_page":"190"},"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9973000288009644,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9919999837875366,"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":0.7442232370376587},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.6321885585784912},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.6277751922607422},{"id":"https://openalex.org/keywords/endomorphism","display_name":"Endomorphism","score":0.5742945075035095},{"id":"https://openalex.org/keywords/congruence-relation","display_name":"Congruence relation","score":0.5362856388092041},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5130389928817749},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.5037049651145935},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46274426579475403},{"id":"https://openalex.org/keywords/disjoint-union","display_name":"Disjoint union (topology)","score":0.4149004817008972},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3447355031967163},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3359401226043701},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1744583249092102},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.12555432319641113},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.0795854926109314}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7442232370376587},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.6321885585784912},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.6277751922607422},{"id":"https://openalex.org/C116858840","wikidata":"https://www.wikidata.org/wiki/Q1340800","display_name":"Endomorphism","level":2,"score":0.5742945075035095},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.5362856388092041},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5130389928817749},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.5037049651145935},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46274426579475403},{"id":"https://openalex.org/C7655956","wikidata":"https://www.wikidata.org/wiki/Q5282259","display_name":"Disjoint union (topology)","level":2,"score":0.4149004817008972},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3447355031967163},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3359401226043701},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1744583249092102},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.12555432319641113},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.0795854926109314},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169708804583","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169708804583","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6000000238418579,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1533648993","https://openalex.org/W1978057069","https://openalex.org/W2018291282","https://openalex.org/W2081974394"],"related_works":["https://openalex.org/W1983745639","https://openalex.org/W2950141706","https://openalex.org/W2141545539","https://openalex.org/W1965531865","https://openalex.org/W2099310349","https://openalex.org/W1974626062","https://openalex.org/W2401586919","https://openalex.org/W2275545295","https://openalex.org/W4381706435","https://openalex.org/W1602210665"],"abstract_inverted_index":{"In":[0,40,109],"[Harr,":[1],"\u203294],":[2],"it":[3,46,115],"was":[4],"shown":[5,49,118,177],"that":[6,50,119,178,218],"every":[7,25],"regular":[8],"language":[9,55,78,96],"and":[10,56,79,133,136,194],"its":[11,80],"complement":[12],"is":[13,22,103,129],"refined":[14],"by":[15,24,105],"a":[16,28,53,86,106],"congruence":[17,200],"of":[18,27,43,59,76,88,112,122,148,151,160,166,169,181,184,191,198,212,224,232],"finite":[19,73,185,196],"index":[20,186,193],"which":[21,67,93,102,225],"preserved":[23,104],"endomorphism":[26,58],"given":[29,107],"finitely-generated":[30],"free":[31,61],"monoid.":[32],"Moreover,":[33],"this":[34,44,113,120,149,161,167,213,230],"refinement":[35,75,101],"can":[36],"be":[37,48,117,126,154,172,176],"algorithmically":[38],"constructed.":[39],"section":[41,110,158,210],"one":[42],"paper,":[45,114,162],"will":[47,125,171],"there":[51,68],"exists":[52],"linear":[54],"an":[57,99],"the":[60,77,89,95,206],"monoid":[62],"on":[63],"two":[64,111,211],"generators":[65],"in":[66,92,141,157,205,209,229],"does":[69],"not":[70,137],"exist":[71],"any":[72],"morphic":[74,188],"complement.":[81],"The":[82],"aforementioned":[83],"example":[84],"motivates":[85],"weakening":[87],"above":[90],"hypotheses":[91],"only":[94],"itself":[97],"has":[98],"algorithmically-constructable":[100],"endomorphism.":[108],"shall":[116,153,175],"class":[121,150,168,207,231],"languages":[123,152,170,204,222],"(which":[124],"denoted":[127],"EndPres)":[128],"closed":[130,138],"under":[131,139],"intersection":[132],"disjoint":[134],"union":[135],"complementation":[140],"many":[142],"instances.":[143],"Also,":[144],"some":[145,163,219],"decidable":[146],"properties":[147],"given.":[155],"Finally,":[156,215],"three":[159],"nonregular":[164,203,221],"members":[165],"examined.":[173],"It":[174],"standard":[179],"extensions":[180],"subword-counting":[182],"congruences":[183],"induce":[187],"equivalence":[189],"relations":[190],"infinite":[192],"so":[195],"unions":[197],"these":[199],"classes":[201],"yield":[202],"discussed":[208],"work.":[214],"we'll":[216],"show":[217],"well-known":[220],"(some":[223],"are":[226,228],"context-sensitive)":[227],"languages.":[233]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
