{"id":"https://openalex.org/W4404194047","doi":"https://doi.org/10.1017/s0960129524000276","title":"Optimal approximate minimization of one-letter weighted finite automata","display_name":"Optimal approximate minimization of one-letter weighted finite automata","publication_year":2024,"publication_date":"2024-09-01","ids":{"openalex":"https://openalex.org/W4404194047","doi":"https://doi.org/10.1017/s0960129524000276"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129524000276","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0960129524000276","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9733CA9F3079F9186103F8515DE86D96/S0960129524000276a.pdf/div-class-title-optimal-approximate-minimization-of-one-letter-weighted-finite-automata-div.pdf","source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9733CA9F3079F9186103F8515DE86D96/S0960129524000276a.pdf/div-class-title-optimal-approximate-minimization-of-one-letter-weighted-finite-automata-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011725093","display_name":"Clara Lacroce","orcid":"https://orcid.org/0000-0002-2087-7630"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]},{"id":"https://openalex.org/I4210164802","display_name":"Mila - Quebec Artificial Intelligence Institute","ror":"https://ror.org/05c22rx21","country_code":"CA","type":"facility","lineage":["https://openalex.org/I4210164802"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Clara Lacroce","raw_affiliation_strings":["Mila, Montr\u00e9al, Canada","School of Computer Science, McGill University, Montr\u00e9al, Canada"],"affiliations":[{"raw_affiliation_string":"Mila, Montr\u00e9al, Canada","institution_ids":["https://openalex.org/I4210164802"]},{"raw_affiliation_string":"School of Computer Science, McGill University, Montr\u00e9al, Canada","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085679401","display_name":"Borja Balle","orcid":"https://orcid.org/0009-0003-8726-2803"},"institutions":[{"id":"https://openalex.org/I4210090411","display_name":"DeepMind (United Kingdom)","ror":"https://ror.org/00971b260","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210090411","https://openalex.org/I4210128969"]},{"id":"https://openalex.org/I4210113297","display_name":"Google (United Kingdom)","ror":"https://ror.org/024bc3e07","country_code":"GB","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210113297","https://openalex.org/I4210128969"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Borja Balle","raw_affiliation_strings":["Department of Research, Google DeepMind, London, UK"],"affiliations":[{"raw_affiliation_string":"Department of Research, Google DeepMind, London, UK","institution_ids":["https://openalex.org/I4210113297","https://openalex.org/I4210090411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068822568","display_name":"Prakash Panangaden","orcid":"https://orcid.org/0000-0001-8763-6172"},"institutions":[{"id":"https://openalex.org/I4210164802","display_name":"Mila - Quebec Artificial Intelligence Institute","ror":"https://ror.org/05c22rx21","country_code":"CA","type":"facility","lineage":["https://openalex.org/I4210164802"]},{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Prakash Panangaden","raw_affiliation_strings":["Mila, Montr\u00e9al, Canada","School of Computer Science, McGill University, Montr\u00e9al, Canada"],"affiliations":[{"raw_affiliation_string":"Mila, Montr\u00e9al, Canada","institution_ids":["https://openalex.org/I4210164802"]},{"raw_affiliation_string":"School of Computer Science, McGill University, Montr\u00e9al, Canada","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023766963","display_name":"Guillaume Rabusseau","orcid":"https://orcid.org/0000-0001-8090-2810"},"institutions":[{"id":"https://openalex.org/I70931966","display_name":"Universit\u00e9 de Montr\u00e9al","ror":"https://ror.org/0161xgx34","country_code":"CA","type":"education","lineage":["https://openalex.org/I70931966"]},{"id":"https://openalex.org/I109736498","display_name":"Canadian Institute for Advanced Research","ror":"https://ror.org/01sdtdd95","country_code":"CA","type":"facility","lineage":["https://openalex.org/I109736498"]},{"id":"https://openalex.org/I4210164802","display_name":"Mila - Quebec Artificial Intelligence Institute","ror":"https://ror.org/05c22rx21","country_code":"CA","type":"facility","lineage":["https://openalex.org/I4210164802"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Guillaume Rabusseau","raw_affiliation_strings":["CIFAR AI Chair, Canada","DIRO, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al, Canada","Mila, Montr\u00e9al, Canada"],"affiliations":[{"raw_affiliation_string":"CIFAR AI Chair, Canada","institution_ids":["https://openalex.org/I109736498"]},{"raw_affiliation_string":"DIRO, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al, Canada","institution_ids":["https://openalex.org/I70931966"]},{"raw_affiliation_string":"Mila, Montr\u00e9al, Canada","institution_ids":["https://openalex.org/I4210164802"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5011725093"],"corresponding_institution_ids":["https://openalex.org/I4210164802","https://openalex.org/I5023651"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24201713,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"8","first_page":"807","last_page":"833"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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":0.9998999834060669,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9997000098228455,"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/T10142","display_name":"Formal Methods in Verification","score":0.9977999925613403,"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/minification","display_name":"Minification","score":0.6715216636657715},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.5778829455375671},{"id":"https://openalex.org/keywords/dfa-minimization","display_name":"DFA minimization","score":0.5362640619277954},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5309186577796936},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41032010316848755},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34810155630111694},{"id":"https://openalex.org/keywords/nondeterministic-finite-automaton","display_name":"Nondeterministic finite automaton","score":0.3075186312198639},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2514914870262146},{"id":"https://openalex.org/keywords/automata-theory","display_name":"Automata theory","score":0.2154727578163147},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.17116102576255798}],"concepts":[{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6715216636657715},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.5778829455375671},{"id":"https://openalex.org/C65753522","wikidata":"https://www.wikidata.org/wiki/Q5204896","display_name":"DFA minimization","level":5,"score":0.5362640619277954},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5309186577796936},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41032010316848755},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34810155630111694},{"id":"https://openalex.org/C158008952","wikidata":"https://www.wikidata.org/wiki/Q617295","display_name":"Nondeterministic finite automaton","level":4,"score":0.3075186312198639},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2514914870262146},{"id":"https://openalex.org/C116248031","wikidata":"https://www.wikidata.org/wiki/Q214526","display_name":"Automata theory","level":3,"score":0.2154727578163147},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.17116102576255798}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0960129524000276","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0960129524000276","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9733CA9F3079F9186103F8515DE86D96/S0960129524000276a.pdf/div-class-title-optimal-approximate-minimization-of-one-letter-weighted-finite-automata-div.pdf","source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1017/s0960129524000276","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0960129524000276","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9733CA9F3079F9186103F8515DE86D96/S0960129524000276a.pdf/div-class-title-optimal-approximate-minimization-of-one-letter-weighted-finite-automata-div.pdf","source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.4000000059604645,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4404194047.pdf"},"referenced_works_count":65,"referenced_works":["https://openalex.org/W164910094","https://openalex.org/W347217945","https://openalex.org/W560247932","https://openalex.org/W1493925387","https://openalex.org/W1547922676","https://openalex.org/W1551480811","https://openalex.org/W1643571618","https://openalex.org/W1825640910","https://openalex.org/W1967332578","https://openalex.org/W1971754347","https://openalex.org/W1974087541","https://openalex.org/W1984065242","https://openalex.org/W1984714339","https://openalex.org/W1988520274","https://openalex.org/W1992363721","https://openalex.org/W2004026774","https://openalex.org/W2014882046","https://openalex.org/W2023369354","https://openalex.org/W2059144133","https://openalex.org/W2059783448","https://openalex.org/W2064675550","https://openalex.org/W2078868580","https://openalex.org/W2079886164","https://openalex.org/W2081504050","https://openalex.org/W2088748973","https://openalex.org/W2095539922","https://openalex.org/W2118901376","https://openalex.org/W2135090412","https://openalex.org/W2153204066","https://openalex.org/W2156429182","https://openalex.org/W2171773189","https://openalex.org/W2178359813","https://openalex.org/W2228143038","https://openalex.org/W2291091846","https://openalex.org/W2314434379","https://openalex.org/W2316950644","https://openalex.org/W2671562901","https://openalex.org/W2679947596","https://openalex.org/W2768277027","https://openalex.org/W2809900044","https://openalex.org/W2887199107","https://openalex.org/W2945975900","https://openalex.org/W2970738355","https://openalex.org/W2997095483","https://openalex.org/W2997643781","https://openalex.org/W3007254004","https://openalex.org/W3099260962","https://openalex.org/W3103899663","https://openalex.org/W3109694792","https://openalex.org/W3134903385","https://openalex.org/W3140224754","https://openalex.org/W3155101735","https://openalex.org/W3161467646","https://openalex.org/W3170197851","https://openalex.org/W3177420896","https://openalex.org/W4210472623","https://openalex.org/W4233392889","https://openalex.org/W4281760247","https://openalex.org/W4320800818","https://openalex.org/W6608278454","https://openalex.org/W6637494315","https://openalex.org/W6683794572","https://openalex.org/W6815054917","https://openalex.org/W6838982598","https://openalex.org/W7054316933"],"related_works":["https://openalex.org/W3143588635","https://openalex.org/W2030569822","https://openalex.org/W2088578754","https://openalex.org/W1843639509","https://openalex.org/W2000290048","https://openalex.org/W888262983","https://openalex.org/W11319064","https://openalex.org/W1560450186","https://openalex.org/W2136740376","https://openalex.org/W2075835272"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4,41,102],"study":[5],"the":[6,17,28,34,46,52,59,88,91,94,112],"approximate":[7,62],"minimization":[8,63],"problem":[9,35,64],"of":[10,21,30,38,48,90,115],"weighted":[11],"finite":[12],"automata":[13],"(WFAs):":[14],"to":[15,110],"compute":[16,111],"best":[18],"possible":[19],"approximation":[20,47,92,114],"a":[22,25,73,78,104,116],"WFA":[23],"given":[24,117],"bound":[26],"on":[27,45,82,87],"number":[29],"states.":[31],"By":[32],"reformulating":[33],"in":[36,93,119],"terms":[37],"Hankel":[39,49],"matrices,":[40],"leverage":[42],"classical":[43],"results":[44],"operators,":[50],"namely":[51],"celebrated":[53],"Adamyan-Arov-Krein":[54],"(AAK)":[55],"theory.":[56],"We":[57,76],"solve":[58],"optimal":[60,113],"spectral-norm":[61],"for":[65],"irredundant":[66],"WFAs":[67],"with":[68],"real":[69],"weights,":[70],"defined":[71],"over":[72],"one-letter":[74],"alphabet.":[75],"present":[77],"theoretical":[79],"analysis":[80],"based":[81],"AAK":[83],"theory":[84],"and":[85,97,107],"bounds":[86],"quality":[89],"spectral":[95],"norm":[96],"$\\ell":[98],"^2$":[99],"norm.":[100],"Moreover,":[101],"provide":[103],"closed-form":[105],"solution,":[106],"an":[108],"algorithm,":[109],"size":[118],"polynomial":[120],"time.":[121]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}