{"id":"https://openalex.org/W4383554657","doi":"https://doi.org/10.1145/3607471","title":"Co-lexicographically Ordering Automata and Regular Languages - Part I","display_name":"Co-lexicographically Ordering Automata and Regular Languages - Part I","publication_year":2023,"publication_date":"2023-07-07","ids":{"openalex":"https://openalex.org/W4383554657","doi":"https://doi.org/10.1145/3607471"},"language":"en","primary_location":{"id":"doi:10.1145/3607471","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3607471","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/10278/5049062","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024275216","display_name":"Nicola Cotumaccio","orcid":"https://orcid.org/0000-0002-1402-5298"},"institutions":[{"id":"https://openalex.org/I129902397","display_name":"Dalhousie University","ror":"https://ror.org/01e6qks80","country_code":"CA","type":"education","lineage":["https://openalex.org/I129902397"]},{"id":"https://openalex.org/I4210150763","display_name":"Gran Sasso Science Institute","ror":"https://ror.org/043qcb444","country_code":"IT","type":"education","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210150763"]}],"countries":["CA","IT"],"is_corresponding":true,"raw_author_name":"Nicola Cotumaccio","raw_affiliation_strings":["Gran Sasso Science Institute, Italy and Dalhousie University, Canada"],"raw_orcid":"https://orcid.org/0000-0002-1402-5298","affiliations":[{"raw_affiliation_string":"Gran Sasso Science Institute, Italy and Dalhousie University, Canada","institution_ids":["https://openalex.org/I4210150763","https://openalex.org/I129902397"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038012736","display_name":"Giovanna D\u2019Agostino","orcid":"https://orcid.org/0000-0002-8920-483X"},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giovanna D\u2019Agostino","raw_affiliation_strings":["University of Udine, Italy"],"raw_orcid":"https://orcid.org/0000-0002-8920-483X","affiliations":[{"raw_affiliation_string":"University of Udine, Italy","institution_ids":["https://openalex.org/I129043915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042115100","display_name":"Alberto Policriti","orcid":"https://orcid.org/0000-0001-8502-5896"},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alberto Policriti","raw_affiliation_strings":["University of Udine, Italy"],"raw_orcid":"https://orcid.org/0000-0001-8502-5896","affiliations":[{"raw_affiliation_string":"University of Udine, Italy","institution_ids":["https://openalex.org/I129043915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007324430","display_name":"Nicola Prezza","orcid":"https://orcid.org/0000-0003-3553-4953"},"institutions":[{"id":"https://openalex.org/I149461666","display_name":"Ca' Foscari University of Venice","ror":"https://ror.org/04yzxz566","country_code":"IT","type":"education","lineage":["https://openalex.org/I149461666"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Nicola Prezza","raw_affiliation_strings":["Ca\u2019 Foscari University of Venice, Italy","Ca' Foscari University of Venice, Italy"],"raw_orcid":"https://orcid.org/0000-0003-3553-4953","affiliations":[{"raw_affiliation_string":"Ca\u2019 Foscari University of Venice, Italy","institution_ids":["https://openalex.org/I149461666"]},{"raw_affiliation_string":"Ca' Foscari University of Venice, Italy","institution_ids":["https://openalex.org/I149461666"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5024275216"],"corresponding_institution_ids":["https://openalex.org/I129902397","https://openalex.org/I4210150763"],"apc_list":null,"apc_paid":null,"fwci":2.091,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.8903443,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"70","issue":"4","first_page":"1","last_page":"73"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998000264167786,"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":0.9998000264167786,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.9987000226974487,"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/T12326","display_name":"Network Packet Processing and Optimization","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/lexicographical-order","display_name":"Lexicographical order","score":0.7562308311462402},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.5763687491416931},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5606536865234375},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.5507489442825317},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5380840301513672},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5308495759963989},{"id":"https://openalex.org/keywords/nondeterministic-finite-automaton","display_name":"Nondeterministic finite automaton","score":0.5102438926696777},{"id":"https://openalex.org/keywords/\u03c9-automaton","display_name":"\u03c9-automaton","score":0.4972217381000519},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48548629879951477},{"id":"https://openalex.org/keywords/prefix","display_name":"Prefix","score":0.4838325083255768},{"id":"https://openalex.org/keywords/deterministic-automaton","display_name":"Deterministic automaton","score":0.4698081612586975},{"id":"https://openalex.org/keywords/regular-expression","display_name":"Regular expression","score":0.4581202268600464},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44598615169525146},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.443767786026001},{"id":"https://openalex.org/keywords/nested-word","display_name":"Nested word","score":0.4375641345977783},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.42356327176094055},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.4025886654853821},{"id":"https://openalex.org/keywords/quantum-finite-automata","display_name":"Quantum finite automata","score":0.3772827386856079},{"id":"https://openalex.org/keywords/automata-theory","display_name":"Automata theory","score":0.36720338463783264},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3168056607246399},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2679508924484253},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.13984650373458862}],"concepts":[{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.7562308311462402},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.5763687491416931},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5606536865234375},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.5507489442825317},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5380840301513672},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5308495759963989},{"id":"https://openalex.org/C158008952","wikidata":"https://www.wikidata.org/wiki/Q617295","display_name":"Nondeterministic finite automaton","level":4,"score":0.5102438926696777},{"id":"https://openalex.org/C92710233","wikidata":"https://www.wikidata.org/wiki/Q291256","display_name":"\u03c9-automaton","level":5,"score":0.4972217381000519},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48548629879951477},{"id":"https://openalex.org/C141603448","wikidata":"https://www.wikidata.org/wiki/Q134830","display_name":"Prefix","level":2,"score":0.4838325083255768},{"id":"https://openalex.org/C194525867","wikidata":"https://www.wikidata.org/wiki/Q5265707","display_name":"Deterministic automaton","level":3,"score":0.4698081612586975},{"id":"https://openalex.org/C121329065","wikidata":"https://www.wikidata.org/wiki/Q185612","display_name":"Regular expression","level":2,"score":0.4581202268600464},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44598615169525146},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.443767786026001},{"id":"https://openalex.org/C92117001","wikidata":"https://www.wikidata.org/wiki/Q6997829","display_name":"Nested word","level":5,"score":0.4375641345977783},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.42356327176094055},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.4025886654853821},{"id":"https://openalex.org/C174327141","wikidata":"https://www.wikidata.org/wiki/Q176837","display_name":"Quantum finite automata","level":4,"score":0.3772827386856079},{"id":"https://openalex.org/C116248031","wikidata":"https://www.wikidata.org/wiki/Q214526","display_name":"Automata theory","level":3,"score":0.36720338463783264},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3168056607246399},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2679508924484253},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.13984650373458862},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3607471","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3607471","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},{"id":"pmh:oai:iris.unive.it:10278/5049062","is_oa":true,"landing_page_url":"https://hdl.handle.net/10278/5049062","pdf_url":null,"source":{"id":"https://openalex.org/S4306402336","display_name":"ARCA (Universit\u00e0 Ca' Foscari Venezia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149461666","host_organization_name":"Ca' Foscari University of Venice","host_organization_lineage":["https://openalex.org/I149461666"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:iris.unive.it:10278/5049062","is_oa":true,"landing_page_url":"https://hdl.handle.net/10278/5049062","pdf_url":null,"source":{"id":"https://openalex.org/S4306402336","display_name":"ARCA (Universit\u00e0 Ca' Foscari Venezia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149461666","host_organization_name":"Ca' Foscari University of Venice","host_organization_lineage":["https://openalex.org/I149461666"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.5199999809265137,"display_name":"Quality Education"}],"awards":[{"id":"https://openalex.org/G3945328635","display_name":null,"funder_award_id":"REGINDEX, 101039208","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4796760706","display_name":null,"funder_award_id":"101039208","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5538627578","display_name":null,"funder_award_id":"CN_00000033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8036287153","display_name":null,"funder_award_id":"Project code CN_00000033","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":73,"referenced_works":["https://openalex.org/W6247929","https://openalex.org/W1489130842","https://openalex.org/W1489366126","https://openalex.org/W1491614438","https://openalex.org/W1516961187","https://openalex.org/W1521674074","https://openalex.org/W1548501023","https://openalex.org/W1548702063","https://openalex.org/W1582690601","https://openalex.org/W1764956874","https://openalex.org/W1867886327","https://openalex.org/W1973883768","https://openalex.org/W1985572324","https://openalex.org/W1986058515","https://openalex.org/W1987760161","https://openalex.org/W1988115395","https://openalex.org/W1992751852","https://openalex.org/W1998084650","https://openalex.org/W2010487137","https://openalex.org/W2011210839","https://openalex.org/W2019522567","https://openalex.org/W2076872551","https://openalex.org/W2094423121","https://openalex.org/W2114507260","https://openalex.org/W2116250539","https://openalex.org/W2118486794","https://openalex.org/W2144938689","https://openalex.org/W2158322625","https://openalex.org/W2161488606","https://openalex.org/W2164107415","https://openalex.org/W2393727648","https://openalex.org/W2528068670","https://openalex.org/W2547063853","https://openalex.org/W2563724038","https://openalex.org/W2725379159","https://openalex.org/W2750884281","https://openalex.org/W2889833303","https://openalex.org/W2899216981","https://openalex.org/W2960871920","https://openalex.org/W2963315614","https://openalex.org/W2964091527","https://openalex.org/W2964439228","https://openalex.org/W2966735921","https://openalex.org/W2999295646","https://openalex.org/W3038444735","https://openalex.org/W3081483715","https://openalex.org/W3081820491","https://openalex.org/W3089568060","https://openalex.org/W3114237669","https://openalex.org/W3114260090","https://openalex.org/W3126170517","https://openalex.org/W3133800261","https://openalex.org/W3142009789","https://openalex.org/W3159492355","https://openalex.org/W3209919026","https://openalex.org/W3214887360","https://openalex.org/W4205775169","https://openalex.org/W4206480194","https://openalex.org/W4206998859","https://openalex.org/W4237974048","https://openalex.org/W4247564011","https://openalex.org/W4247794781","https://openalex.org/W4254807835","https://openalex.org/W4283805622","https://openalex.org/W4283811431","https://openalex.org/W4302339081","https://openalex.org/W4310061560","https://openalex.org/W4311727100","https://openalex.org/W4317213941","https://openalex.org/W4386870880","https://openalex.org/W4403517675","https://openalex.org/W6766266255","https://openalex.org/W6910373472"],"related_works":["https://openalex.org/W2537940722","https://openalex.org/W4205935260","https://openalex.org/W2368684504","https://openalex.org/W4386400090","https://openalex.org/W1975910189","https://openalex.org/W2160879187","https://openalex.org/W2371400076","https://openalex.org/W2066393902","https://openalex.org/W3143588635","https://openalex.org/W2169203237"],"abstract_inverted_index":{"The":[0],"states":[1,87,394,434],"of":[2,12,18,55,74,86,95,110,163,177,179,204,213,275,279,318,376,395,414,433,435,445],"a":[3,36,53,72,78,107,147,233,255,322,364,369,383,436],"finite-state":[4],"automaton":[5,320,374],"\ud835\udca9":[6],"can":[7,27,133,154,166,242],"be":[8,28,115,134,156,167,243,378],"identified":[9],"with":[10,410],"collections":[11],"words":[13,26,59],"in":[14,67,71,123,228,237,264,291,382],"the":[15,19,32,41,48,56,61,141,173,187,202,238,299,315,358,372,386,393,411,420,427,431,446],"prefix":[16],"closure":[17],"regular":[20,119,260,300,342,452],"language":[21,370],"accepted":[22],"by":[23,328,344],"\ud835\udca9.":[24],"But":[25],"ordered,":[29,158],"and":[30,70,91,117,159,169,294,334,350,361,429],"among":[31],"many":[33],"possible":[34,388],"orders":[35,184],"very":[37],"natural":[38],"one":[39,178],"is":[40,226,321],"co-lexicographic":[42,80],"order.":[43],"Such":[44,93],"naturalness":[45],"stems":[46],"from":[47,58,339],"fact":[49],"that":[50,151,195,282,314,363],"it":[51],"suggests":[52],"transfer":[54],"order":[57,392,413],"to":[60,104,114,267,341,390,405],"automaton\u2019s":[62,188],"states.":[63],"This":[64],"suggestion":[65],"is,":[66],"fact,":[68],"concrete":[69],"number":[73,109,432],"articles":[75],"automata":[76,97,100,132,153,280,340],"admitting":[77],"total":[79],"(":[81],"co-lex":[82,182,189,214,316],"for":[83,298,307,449],"brevity)":[84],"ordering":[85],"have":[88],"been":[89],"proposed":[90],"studied.":[92],"class":[94],"ordered":[96,136,451],"\u2014":[98,101],"Wheeler":[99],"turned":[102],"out":[103,146],"require":[105],"just":[106,246],"constant":[108,124],"bits":[111,250],"per":[112,126,251,270],"transition":[113],"represented":[116],"enable":[118],"expression":[120,261,301],"matching":[121,262,302],"queries":[122,263],"time":[125,265],"matched":[127,271],"character.":[128,272],"Unfortunately,":[129],"not":[130,305],"all":[131,152],"totally":[135],"as":[137,286,400,402],"previously":[138],"outlined.":[139],"In":[140,352,438],"present":[142],"work,":[143],"we":[144,326,355,403,418,441],"lay":[145],"new":[148,197,277],"theory":[149],"showing":[150],"always":[155],"partially":[157],"an":[160,220,319,407,443],"intrinsic":[161],"measure":[162,198],"their":[164,180,346],"complexity":[165,203,324,333],"defined":[168],"effectively":[170],"determined,":[171],"namely,":[172],"minimum":[174],"width":[175,190,215,317,428],"p":[176,216,229,248,268,292,310],"admissible":[181],"partial":[183],"\u2013dubbed":[185],"here":[186],".":[191,311],"We":[192],"first":[193],"show":[194],"this":[196,276,337,353,439],"captures":[199],"at":[200],"once":[201],"several":[205],"seemingly-unrelated":[206],"hard":[207],"problems":[208,284],"on":[209,357],"automata.":[210],"Any":[211],"NFA":[212,287],":":[217],"(i)":[218,329],"has":[219],"equivalent":[221],"powerset":[222],"DFA":[223,367,397],"whose":[224],"size":[225],"exponential":[227],"rather":[230],"than":[231],"(as":[232],"classic":[234],"analysis":[235],"shows)":[236],"NFA\u2019s":[239],"size;":[240],"(ii)":[241,335],"encoded":[244],"using":[245],"\u0398(log":[247],")":[249],"transition;":[252],"(iii)":[253],"admits":[254],"linear-space":[256],"data":[257],"structure":[258],"solving":[259],"proportional":[266],"2":[269],"Some":[273],"consequences":[274],"parameterization":[278],"are":[281,289],"PSPACE-hard":[283],"such":[285],"equivalence":[288],"FPT":[290],",":[293],"quadratic":[295],"lower":[296],"bounds":[297],"problem":[303],"do":[304],"hold":[306],"sufficiently":[308],"small":[309],"Having":[312],"established":[313],"fundamental":[323],"measure,":[325],"proceed":[327],"determining":[330],"its":[331],"computational":[332],"extending":[336],"notion":[338],"languages":[343],"studying":[345],"smallest-width":[347],"accepting":[348,368,398],"NFAs":[349],"DFAs.":[351],"work":[354],"focus":[356],"deterministic":[359],"case":[360],"prove":[362],"canonical":[365],"minimum-width":[366],"\u2112\u2013dubbed":[371],"Hasse":[373],"\u210b":[375,380],"\u2112\u2013can":[377],"exhibited.":[379],"provides,":[381],"precise":[384],"sense,":[385],"best":[387],"way":[389],"(partially)":[391],"any":[396],"\u2112,":[399],"long":[401],"want":[404],"maintain":[406],"operational":[408],"link":[409],"(co-lexicographic)":[412],"\u2112\u2019s":[415],"prefixes.":[416],"Finally,":[417],"explore":[419],"relationship":[421],"between":[422],"two":[423],"conflicting":[424],"objectives:":[425],"minimizing":[426,430],"DFA.":[437],"context,":[440],"provide":[442],"analogue":[444],"Myhill-Nerode":[447],"Theorem":[448],"co-lexicographically":[450],"languages.":[453]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}