{"id":"https://openalex.org/W1988857989","doi":"https://doi.org/10.1142/s0129054108005644","title":"ON THE COMPUTATION OF THE RELATIVE ENTROPY OF PROBABILISTIC AUTOMATA","display_name":"ON THE COMPUTATION OF THE RELATIVE ENTROPY OF PROBABILISTIC AUTOMATA","publication_year":2008,"publication_date":"2008-02-01","ids":{"openalex":"https://openalex.org/W1988857989","doi":"https://doi.org/10.1142/s0129054108005644","mag":"1988857989"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054108005644","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054108005644","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/A5013243115","display_name":"Corinna Cortes","orcid":null},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"CORINNA CORTES","raw_affiliation_strings":["Google Research, 76 Ninth Avenue, New York, NY 10011, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google Research, 76 Ninth Avenue, New York, NY 10011, USA","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058849006","display_name":"Mehryar Mohri","orcid":"https://orcid.org/0000-0002-3987-9847"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]},{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"MEHRYAR MOHRI","raw_affiliation_strings":["Courant Institute of Mathematical Sciences and Google Research, 251 Mercer Street, New York, NY 10012, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences and Google Research, 251 Mercer Street, New York, NY 10012, USA","institution_ids":["https://openalex.org/I1291425158","https://openalex.org/I36672615"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059882866","display_name":"Ashish Rastogi","orcid":"https://orcid.org/0000-0002-2412-6770"},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"ASHISH RASTOGI","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA","Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA","institution_ids":["https://openalex.org/I36672615"]},{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA#TAB#","institution_ids":["https://openalex.org/I36672615"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014137885","display_name":"Michael Riley","orcid":"https://orcid.org/0009-0002-9449-025X"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"MICHAEL RILEY","raw_affiliation_strings":["Google Research, 76 Ninth Avenue, New York, NY 10011, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google Research, 76 Ninth Avenue, New York, NY 10011, USA","institution_ids":["https://openalex.org/I1291425158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.7413,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.94274579,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"19","issue":"01","first_page":"219","last_page":"242"},"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":0.9997000098228455,"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":0.9934999942779541,"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":0.6381484270095825},{"id":"https://openalex.org/keywords/probabilistic-automaton","display_name":"Probabilistic automaton","score":0.6131374835968018},{"id":"https://openalex.org/keywords/quantum-finite-automata","display_name":"Quantum finite automata","score":0.5783690810203552},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.48491817712783813},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.4392608106136322},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4370441138744354},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.416128933429718},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3792995810508728},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.3745369017124176},{"id":"https://openalex.org/keywords/automata-theory","display_name":"Automata theory","score":0.3292348384857178},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.27832305431365967},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25190573930740356},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.14766481518745422}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6381484270095825},{"id":"https://openalex.org/C174784677","wikidata":"https://www.wikidata.org/wiki/Q176567","display_name":"Probabilistic automaton","level":3,"score":0.6131374835968018},{"id":"https://openalex.org/C174327141","wikidata":"https://www.wikidata.org/wiki/Q176837","display_name":"Quantum finite automata","level":4,"score":0.5783690810203552},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.48491817712783813},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.4392608106136322},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4370441138744354},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.416128933429718},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3792995810508728},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.3745369017124176},{"id":"https://openalex.org/C116248031","wikidata":"https://www.wikidata.org/wiki/Q214526","display_name":"Automata theory","level":3,"score":0.3292348384857178},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.27832305431365967},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25190573930740356},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.14766481518745422},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054108005644","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054108005644","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":[{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320338478","display_name":"U.S. Army Medical Research Acquisition Activity","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W15573929","https://openalex.org/W138349765","https://openalex.org/W177913229","https://openalex.org/W179694669","https://openalex.org/W605575788","https://openalex.org/W1506437980","https://openalex.org/W1546312364","https://openalex.org/W1549664537","https://openalex.org/W1578332044","https://openalex.org/W1607161872","https://openalex.org/W1860547055","https://openalex.org/W1982330578","https://openalex.org/W1998167411","https://openalex.org/W2009570821","https://openalex.org/W2037047069","https://openalex.org/W2039829163","https://openalex.org/W2046932483","https://openalex.org/W2055664797","https://openalex.org/W2077478451","https://openalex.org/W2090879738","https://openalex.org/W2099111195","https://openalex.org/W2102122585","https://openalex.org/W2125528794","https://openalex.org/W2125529971","https://openalex.org/W2131236363","https://openalex.org/W2159902206","https://openalex.org/W2164715647","https://openalex.org/W2167954650","https://openalex.org/W2752885492","https://openalex.org/W2798909945","https://openalex.org/W3119651796","https://openalex.org/W4212875940","https://openalex.org/W4213269876","https://openalex.org/W4232724009","https://openalex.org/W4245668478"],"related_works":["https://openalex.org/W2953483754","https://openalex.org/W1550824632","https://openalex.org/W2963823488","https://openalex.org/W2950563206","https://openalex.org/W2159449605","https://openalex.org/W2058117339","https://openalex.org/W4300232377","https://openalex.org/W1979390054","https://openalex.org/W201862490","https://openalex.org/W1524267824"],"abstract_inverted_index":{"We":[0,17,71,108],"present":[1],"an":[2,39,187,209,223],"exhaustive":[3],"analysis":[4],"of":[5,8,13,22,27,58,63,77,81,95,105,112,132,163,186,193,205,208,219,222,241,246],"the":[6,10,20,24,56,61,75,78,103,110,113,137,161,172,184,191,203,206,217,220,239,242],"problem":[7,21,37],"computing":[9,23],"relative":[11,25,79,88,115,139,174],"entropy":[12,26,80,89,116,140,175,207],"two":[14,106],"probabilistic":[15,29,83,211,225,248],"automata.":[16,70],"show":[18,122,198],"that":[19,52,74,135,199],"unambiguous":[28,210,224],"automata":[30,84],"can":[31,213],"be":[32,214],"formulated":[33],"as":[34,179,183,189],"a":[35,93,130,180,229,247],"shortest-distance":[36],"over":[38],"appropriate":[40],"semiring,":[41],"give":[42],"efficient":[43,236],"exact":[44],"and":[45,54,99,121,154],"approximate":[46],"algorithms":[47,65,98,120,167,237],"for":[48,66,165,202,238],"its":[49,152],"computation":[50,76,204,218,240],"in":[51,92,117,134,156,190],"case,":[53],"report":[55],"results":[57],"experiments":[59],"demonstrating":[60],"practicality":[62],"our":[64,200],"very":[67],"large":[68],"weighted":[69],"also":[72],"prove":[73],"arbitrary":[82],"is":[85,90,127,141,168,176],"PSPACE-complete.":[86],"The":[87],"used":[91,177],"variety":[94],"machine":[96,118],"learning":[97,119,166],"applications":[100],"to":[101,125,216],"measure":[102],"discrepancy":[104],"distributions.":[107],"examine":[109],"use":[111,153],"symmetrized":[114,138,173],"that,":[123],"contrarily":[124],"what":[126],"suggested":[128],"by":[129,227],"number":[131],"publications":[133],"domain,":[136],"neither":[142],"positive":[143],"definite":[144,148],"symmetric":[145],"nor":[146],"negative":[147],"symmetric,":[149],"which":[150],"limits":[151],"application":[155],"kernel":[157],"methods.":[158],"In":[159,232],"particular,":[160,233],"convergence":[162],"training":[164],"not":[169],"guaranteed":[170],"when":[171],"directly":[178],"kernel,":[181],"or":[182],"operand":[185],"exponential":[188],"case":[192],"Gaussian":[194],"Kernels.":[195],"Finally,":[196],"we":[197],"algorithm":[201],"automaton":[212,226],"generalized":[215],"norm":[221],"using":[228],"monoid":[230],"morphism.":[231],"this":[234],"yields":[235],"L":[243],"p":[244],"-norm":[245],"automaton.":[249]},"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}