{"id":"https://openalex.org/W1876652099","doi":"https://doi.org/10.1007/3-540-44880-2_16","title":"Probabilistic Invariants for Probabilistic Machines","display_name":"Probabilistic Invariants for Probabilistic Machines","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1876652099","doi":"https://doi.org/10.1007/3-540-44880-2_16","mag":"1876652099"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-44880-2_16","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-44880-2_16","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5042805366","display_name":"Thai Son Hoang","orcid":"https://orcid.org/0000-0003-4095-0732"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Thai Son Hoang","raw_affiliation_strings":["School of Computer Science & Engineering, University of New South Wales, NSW, 2052, Australia"],"affiliations":[{"raw_affiliation_string":"School of Computer Science & Engineering, University of New South Wales, NSW, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000992689","display_name":"Zhendong Jin","orcid":null},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Zhendong Jin","raw_affiliation_strings":["School of Computer Science & Engineering, University of New South Wales, NSW, 2052, Australia"],"affiliations":[{"raw_affiliation_string":"School of Computer Science & Engineering, University of New South Wales, NSW, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008417830","display_name":"Ken Robinson","orcid":null},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Ken Robinson","raw_affiliation_strings":["School of Computer Science & Engineering, University of New South Wales, NSW, 2052, Australia"],"affiliations":[{"raw_affiliation_string":"School of Computer Science & Engineering, University of New South Wales, NSW, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035107880","display_name":"Annabelle McIver","orcid":"https://orcid.org/0000-0002-2405-9838"},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Annabelle McIver","raw_affiliation_strings":["Department of Computing, Macquarie University, NSW, 2109, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Computing, Macquarie University, NSW, 2109, Australia","institution_ids":["https://openalex.org/I99043593"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039019347","display_name":"Carroll Morgan","orcid":"https://orcid.org/0000-0002-8535-9068"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Carroll Morgan","raw_affiliation_strings":["School of Computer Science & Engineering, University of New South Wales, NSW, 2052, Australia"],"affiliations":[{"raw_affiliation_string":"School of Computer Science & Engineering, University of New South Wales, NSW, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5042805366"],"corresponding_institution_ids":["https://openalex.org/I31746571"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":2.4885,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.8888543,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"240","last_page":"259"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9993000030517578,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9993000030517578,"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":0.9984999895095825,"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":0.9983999729156494,"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/probabilistic-logic","display_name":"Probabilistic logic","score":0.9087525606155396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7397001385688782},{"id":"https://openalex.org/keywords/probabilistic-argumentation","display_name":"Probabilistic argumentation","score":0.6487528085708618},{"id":"https://openalex.org/keywords/probabilistic-relevance-model","display_name":"Probabilistic relevance model","score":0.5978679060935974},{"id":"https://openalex.org/keywords/probabilistic-ctl","display_name":"Probabilistic CTL","score":0.59501051902771},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5340579748153687},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.45432746410369873},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.43967100977897644},{"id":"https://openalex.org/keywords/probabilistic-database","display_name":"Probabilistic database","score":0.4341360926628113},{"id":"https://openalex.org/keywords/probabilistic-analysis-of-algorithms","display_name":"Probabilistic analysis of algorithms","score":0.4060854911804199},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3533003032207489},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.26896190643310547},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.24598991870880127},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20668742060661316},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.11598709225654602}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.9087525606155396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7397001385688782},{"id":"https://openalex.org/C128828806","wikidata":"https://www.wikidata.org/wiki/Q7246848","display_name":"Probabilistic argumentation","level":3,"score":0.6487528085708618},{"id":"https://openalex.org/C143017306","wikidata":"https://www.wikidata.org/wiki/Q3318133","display_name":"Probabilistic relevance model","level":4,"score":0.5978679060935974},{"id":"https://openalex.org/C52063229","wikidata":"https://www.wikidata.org/wiki/Q7246845","display_name":"Probabilistic CTL","level":4,"score":0.59501051902771},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5340579748153687},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.45432746410369873},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.43967100977897644},{"id":"https://openalex.org/C174539288","wikidata":"https://www.wikidata.org/wiki/Q7246853","display_name":"Probabilistic database","level":4,"score":0.4341360926628113},{"id":"https://openalex.org/C24404364","wikidata":"https://www.wikidata.org/wiki/Q7246846","display_name":"Probabilistic analysis of algorithms","level":3,"score":0.4060854911804199},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3533003032207489},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26896190643310547},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.24598991870880127},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20668742060661316},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.11598709225654602},{"id":"https://openalex.org/C5655090","wikidata":"https://www.wikidata.org/wiki/Q192588","display_name":"Relational database","level":2,"score":0.0},{"id":"https://openalex.org/C5968703","wikidata":"https://www.wikidata.org/wiki/Q267136","display_name":"Database model","level":3,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-44880-2_16","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-44880-2_16","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W405397024","https://openalex.org/W1492315860","https://openalex.org/W1516589479","https://openalex.org/W1545761035","https://openalex.org/W1552647623","https://openalex.org/W1585439950","https://openalex.org/W1600905840","https://openalex.org/W1999355680","https://openalex.org/W2030124942","https://openalex.org/W2141670510","https://openalex.org/W4254354208","https://openalex.org/W4285719527","https://openalex.org/W6632817095"],"related_works":["https://openalex.org/W4238495367","https://openalex.org/W2749065928","https://openalex.org/W2225666389","https://openalex.org/W3132053208","https://openalex.org/W3214184572","https://openalex.org/W3028746955","https://openalex.org/W2471401686","https://openalex.org/W164001702","https://openalex.org/W2104279947","https://openalex.org/W4221154940"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}