{"id":"https://openalex.org/W2113959537","doi":"https://doi.org/10.1007/1-4020-8141-3_26","title":"Precise Analysis of \u03c0-calculus in Cubic Time","display_name":"Precise Analysis of \u03c0-calculus in Cubic Time","publication_year":2006,"publication_date":"2006-02-21","ids":{"openalex":"https://openalex.org/W2113959537","doi":"https://doi.org/10.1007/1-4020-8141-3_26","mag":"2113959537"},"language":"en","primary_location":{"id":"doi:10.1007/1-4020-8141-3_26","is_oa":true,"landing_page_url":"https://doi.org/10.1007/1-4020-8141-3_26","pdf_url":"https://link.springer.com/content/pdf/10.1007/1-4020-8141-3_26.pdf","source":{"id":"https://openalex.org/S4306463519","display_name":"Kluwer Academic Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/1-4020-8141-3_26.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081720287","display_name":"Livio Colussi","orcid":null},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"L. Colussi","raw_affiliation_strings":["Department of Pure and Applied Mathematics, University of Padova, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Pure and Applied Mathematics, University of Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111772084","display_name":"G. Fil\u00e9","orcid":null},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. Fil\u00e8","raw_affiliation_strings":["Department of Pure and Applied Mathematics, University of Padova, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Pure and Applied Mathematics, University of Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038636493","display_name":"Alberto Griggio","orcid":"https://orcid.org/0000-0002-3311-0893"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"A. Griggio","raw_affiliation_strings":["Department of Pure and Applied Mathematics, University of Padova, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Pure and Applied Mathematics, University of Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5081720287"],"corresponding_institution_ids":["https://openalex.org/I138689650"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.19559882,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"317","last_page":"331"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":1.0,"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/T10126","display_name":"Logic, programming, and type systems","score":1.0,"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":0.9995999932289124,"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/T10142","display_name":"Formal Methods in Verification","score":0.9979000091552734,"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/static-analysis","display_name":"Static analysis","score":0.7692397236824036},{"id":"https://openalex.org/keywords/asymptotic-analysis","display_name":"Asymptotic analysis","score":0.5787713527679443},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5332103967666626},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5031113028526306},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.500908374786377},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.45622119307518005},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.344855934381485},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.16584733128547668},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13279783725738525}],"concepts":[{"id":"https://openalex.org/C97686452","wikidata":"https://www.wikidata.org/wiki/Q7604153","display_name":"Static analysis","level":2,"score":0.7692397236824036},{"id":"https://openalex.org/C205147927","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.5787713527679443},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5332103967666626},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5031113028526306},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.500908374786377},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.45622119307518005},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.344855934381485},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.16584733128547668},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13279783725738525},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/1-4020-8141-3_26","is_oa":true,"landing_page_url":"https://doi.org/10.1007/1-4020-8141-3_26","pdf_url":"https://link.springer.com/content/pdf/10.1007/1-4020-8141-3_26.pdf","source":{"id":"https://openalex.org/S4306463519","display_name":"Kluwer Academic Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/1-4020-8141-3_26","is_oa":true,"landing_page_url":"https://doi.org/10.1007/1-4020-8141-3_26","pdf_url":"https://link.springer.com/content/pdf/10.1007/1-4020-8141-3_26.pdf","source":{"id":"https://openalex.org/S4306463519","display_name":"Kluwer Academic Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2113959537.pdf","grobid_xml":"https://content.openalex.org/works/W2113959537.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1485733778","https://openalex.org/W1552110479","https://openalex.org/W1562901937","https://openalex.org/W1567968445","https://openalex.org/W1670563787","https://openalex.org/W1753535896","https://openalex.org/W1863801487","https://openalex.org/W1974152790","https://openalex.org/W2002622794","https://openalex.org/W2008838944","https://openalex.org/W2013672985","https://openalex.org/W2043100293","https://openalex.org/W2049224403","https://openalex.org/W2067359684","https://openalex.org/W2128932399","https://openalex.org/W2168453169","https://openalex.org/W3145128584","https://openalex.org/W6662412777","https://openalex.org/W6990773698"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2317200988","https://openalex.org/W2151320244","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2053286651","https://openalex.org/W1570829627","https://openalex.org/W2181743346","https://openalex.org/W2113959537"],"abstract_inverted_index":{"It":[0],"is":[1,37,69,78],"known":[2],"that":[3,35,67,76,100],"a":[4,24],"static":[5,25,96],"analysis":[6,26,50,97],"of":[7,9,48,61,98],"\u03c0-calculas":[8],"can":[10],"be":[11,28,86],"done":[12],"rather":[13],"simply":[14],"and":[15,72],"also":[16,42,74,88],"efficiently,":[17],"i.e.":[18],"in":[19,92],"O(n":[20],"3)":[21],"time.":[22],"Clearly,":[23],"should":[27],"as":[29,31],"precise":[30],"possible.":[32],"We":[33,56],"show":[34,75],"it":[36,68,77],"not":[38],"only":[39],"desirable,":[40],"but":[41],"possible":[43],"to":[44,85],"improve":[45],"the":[46,49,58,95,102],"precision":[47],"without":[51],"worsening":[52],"its":[53],"asymptotic":[54],"complexity.":[55],"illustrate":[57],"main":[59],"principles":[60],"this":[62],"efficient":[63],"algorithm,":[64],"we":[65,73],"prove":[66],"indeed":[70],"cubic":[71],"correct.":[79],"The":[80],"technique":[81],"introduced":[82],"here":[83],"appears":[84],"useful":[87],"for":[89,94],"other":[90],"applications,":[91],"particular,":[93],"languages":[99],"extend":[101],"\u03c0-calculas.":[103]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}