{"id":"https://openalex.org/W2726753079","doi":"https://doi.org/10.2168/lmcs-4(2:2)2008","title":"Approximating a Behavioural Pseudometric without Discount for Probabilistic Systems","display_name":"Approximating a Behavioural Pseudometric without Discount for Probabilistic Systems","publication_year":2008,"publication_date":"2008-04-09","ids":{"openalex":"https://openalex.org/W2726753079","doi":"https://doi.org/10.2168/lmcs-4(2:2)2008","mag":"2726753079"},"language":"en","primary_location":{"id":"doi:10.2168/lmcs-4(2:2)2008","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-4(2:2)2008","pdf_url":"https://lmcs.episciences.org/822/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/822/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Franck van Breugel","orcid":null},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]},{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["CA","GB"],"is_corresponding":true,"raw_author_name":"Franck van Breugel","raw_affiliation_strings":["Oxford University Computing Laboratory, Parks Road, Oxford, OX1 3QD, England","York University, 4700 Keele Street, Toronto, M3J 1P3, Canada"],"affiliations":[{"raw_affiliation_string":"Oxford University Computing Laboratory, Parks Road, Oxford, OX1 3QD, England","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"York University, 4700 Keele Street, Toronto, M3J 1P3, Canada","institution_ids":["https://openalex.org/I192455969"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Babita Sharma","orcid":null},"institutions":[{"id":"https://openalex.org/I4210113654","display_name":"IBM (Canada)","ror":"https://ror.org/025sxka56","country_code":"CA","type":"company","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210113654"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Babita Sharma","raw_affiliation_strings":["IBM Toronto Lab, 8200 Warden Avenue, Markham, L6G 1C7, Canada"],"affiliations":[{"raw_affiliation_string":"IBM Toronto Lab, 8200 Warden Avenue, Markham, L6G 1C7, Canada","institution_ids":["https://openalex.org/I4210113654"]}]},{"author_position":"last","author":{"id":null,"display_name":"James Worrell","orcid":"https://orcid.org/0000-0001-8151-2443"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"James Worrell","raw_affiliation_strings":["Oxford University Computing Laboratory, Parks Road, Oxford, OX1 3QD, England"],"affiliations":[{"raw_affiliation_string":"Oxford University Computing Laboratory, Parks Road, Oxford, OX1 3QD, England","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I192455969","https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":0.827,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.78390937,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"Volume 4, Issue 2","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.46650001406669617,"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/T10142","display_name":"Formal Methods in Verification","score":0.46650001406669617,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.08860000222921371,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.0738999992609024,"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/probabilistic-logic","display_name":"Probabilistic logic","score":0.8729000091552734},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.6230000257492065},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5751000046730042},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5516999959945679},{"id":"https://openalex.org/keywords/discounting","display_name":"Discounting","score":0.5361999869346619},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44510000944137573},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4429999887943268},{"id":"https://openalex.org/keywords/decision-theory","display_name":"Decision theory","score":0.43639999628067017},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.40950000286102295}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.8729000091552734},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6773999929428101},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6230000257492065},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5751000046730042},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5516999959945679},{"id":"https://openalex.org/C6177178","wikidata":"https://www.wikidata.org/wiki/Q10998070","display_name":"Discounting","level":2,"score":0.5361999869346619},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44510000944137573},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4429999887943268},{"id":"https://openalex.org/C28901747","wikidata":"https://www.wikidata.org/wiki/Q177571","display_name":"Decision theory","level":2,"score":0.43639999628067017},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4140999913215637},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.40950000286102295},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35850000381469727},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.35499998927116394},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3513999879360199},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3481999933719635},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3418999910354614},{"id":"https://openalex.org/C60782215","wikidata":"https://www.wikidata.org/wiki/Q3333679","display_name":"Probabilistic method","level":3,"score":0.33390000462532043},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.32749998569488525},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3237000107765198},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.31189998984336853},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3052000105381012},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.2849000096321106},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2833000123500824},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.27320000529289246},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C24404364","wikidata":"https://www.wikidata.org/wiki/Q7246846","display_name":"Probabilistic analysis of algorithms","level":3,"score":0.27090001106262207},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2522999942302704}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2168/lmcs-4(2:2)2008","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-4(2:2)2008","pdf_url":"https://lmcs.episciences.org/822/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0803.3796","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0803.3796","pdf_url":"https://arxiv.org/pdf/0803.3796","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:d388078649a24eb58546e2f0ea283e2e","is_oa":true,"landing_page_url":"https://doaj.org/article/d388078649a24eb58546e2f0ea283e2e","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 4, Issue 2 (2008)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2168/lmcs-4(2:2)2008","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-4(2:2)2008","pdf_url":"https://lmcs.episciences.org/822/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2726753079.pdf","grobid_xml":"https://content.openalex.org/works/W2726753079.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W62960856","https://openalex.org/W173641204","https://openalex.org/W259536784","https://openalex.org/W1514850456","https://openalex.org/W1523168988","https://openalex.org/W1546768510","https://openalex.org/W1547562281","https://openalex.org/W1551877760","https://openalex.org/W1553142094","https://openalex.org/W1565007974","https://openalex.org/W1813686459","https://openalex.org/W1963619740","https://openalex.org/W1980535239","https://openalex.org/W2001539364","https://openalex.org/W2063972032","https://openalex.org/W2103745248","https://openalex.org/W2107471150","https://openalex.org/W2108489993","https://openalex.org/W2113256684","https://openalex.org/W2126031877","https://openalex.org/W2135115058","https://openalex.org/W2528800419","https://openalex.org/W6631620553","https://openalex.org/W6654384574"],"related_works":[],"abstract_inverted_index":{"Desharnais,":[0],"Gupta,":[1],"Jagadeesan":[2],"and":[3],"Panangaden":[4],"introduced":[5],"a":[6,18,32,35],"family":[7],"of":[8,21,84,115],"behavioural":[9,74],"pseudometrics":[10,16],"for":[11,122,144],"probabilistic":[12,22,27],"transition":[13],"systems.":[14],"These":[15],"are":[17],"quantitative":[19],"analogue":[20],"bisimilarity.":[23,28],"Distance":[24],"zero":[25],"captures":[26],"Each":[29],"pseudometric":[30],"has":[31],"discount":[33,46,56,88],"factor,":[34,47],"real":[36,128],"number":[37],"in":[38],"the":[39,45,48,50,55,61,73,87,100,107,123,133,141],"interval":[40],"(0,":[41],"1].":[42],"The":[43],"smaller":[44,91],"more":[49,146],"future":[51,62,108],"is":[52,58,63,90,109,118],"discounted.":[53,111],"If":[54],"factor":[57,89],"one,":[59],"then":[60],"not":[64,110],"discounted":[65],"at":[66],"all.":[67],"Desharnais":[68],"et":[69],"al.":[70],"showed":[71],"that":[72,99],"distances":[75,101],"can":[76,102,138],"be":[77,104],"calculated":[78],"up":[79],"to":[80,140],"any":[81],"desired":[82],"degree":[83],"accuracy":[85],"if":[86,106],"than":[92],"one.":[93],"In":[94],"this":[95],"paper,":[96],"we":[97,137],"show":[98],"also":[103],"approximated":[105],"A":[112],"key":[113],"ingredient":[114],"our":[116],"algorithm":[117],"Tarski's":[119],"decision":[120,148],"procedure":[121],"first":[124],"order":[125],"theory":[126],"over":[127],"closed":[129],"fields.":[130],"By":[131],"exploiting":[132],"Kantorovich-Rubinstein":[134],"duality":[135],"theorem":[136],"restrict":[139],"existential":[142],"fragment":[143],"which":[145],"efficient":[147],"procedures":[149],"exist.":[150]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2017-07-14T00:00:00"}