{"id":"https://openalex.org/W1525594430","doi":"https://doi.org/10.1007/3-540-36390-4_4","title":"Counting the Solutions of Presburger Equations without Enumerating Them","display_name":"Counting the Solutions of Presburger Equations without Enumerating Them","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1525594430","doi":"https://doi.org/10.1007/3-540-36390-4_4","mag":"1525594430"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-36390-4_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-36390-4_4","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":"conference-paper","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/A5078094550","display_name":"Bernard Boigelot","orcid":"https://orcid.org/0009-0009-4721-3824"},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Bernard Boigelot","raw_affiliation_strings":["Institut Montefiore, B28, Universit\u00e9 de Li\u00e8ge, B-4000, Li\u00e8ge Sart-Tilman, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Montefiore, B28, Universit\u00e9 de Li\u00e8ge, B-4000, Li\u00e8ge Sart-Tilman, Belgium","institution_ids":["https://openalex.org/I157674565"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070797793","display_name":"Louis Latour","orcid":null},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Louis Latour","raw_affiliation_strings":["Institut Montefiore, B28, Universit\u00e9 de Li\u00e8ge, B-4000, Li\u00e8ge Sart-Tilman, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Montefiore, B28, Universit\u00e9 de Li\u00e8ge, B-4000, Li\u00e8ge Sart-Tilman, Belgium","institution_ids":["https://openalex.org/I157674565"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I157674565"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.5136,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.54893479,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"40","last_page":"51"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","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/T12072","display_name":"Machine Learning and Algorithms","score":0.9988999962806702,"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":0.9883000254631042,"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/presburger-arithmetic","display_name":"Presburger arithmetic","score":0.7330601215362549},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6921057105064392},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6707578301429749},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5695258378982544},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5353301763534546},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5205293893814087},{"id":"https://openalex.org/keywords/set-operations","display_name":"Set operations","score":0.46696168184280396},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4445697069168091},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4428715705871582},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.431776762008667},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.376832515001297},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36454999446868896},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.20461881160736084},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.0718647837638855}],"concepts":[{"id":"https://openalex.org/C5852641","wikidata":"https://www.wikidata.org/wiki/Q956059","display_name":"Presburger arithmetic","level":3,"score":0.7330601215362549},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6921057105064392},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6707578301429749},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5695258378982544},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5353301763534546},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5205293893814087},{"id":"https://openalex.org/C2777168461","wikidata":"https://www.wikidata.org/wiki/Q42196253","display_name":"Set operations","level":3,"score":0.46696168184280396},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4445697069168091},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4428715705871582},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.431776762008667},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.376832515001297},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36454999446868896},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.20461881160736084},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0718647837638855},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-36390-4_4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-36390-4_4","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":[{"score":0.8100000023841858,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W113519291","https://openalex.org/W1500263346","https://openalex.org/W1540012118","https://openalex.org/W1597840949","https://openalex.org/W1822301642","https://openalex.org/W1842953027","https://openalex.org/W1963547452","https://openalex.org/W2008644136","https://openalex.org/W2030999998","https://openalex.org/W2046615742","https://openalex.org/W2097699872","https://openalex.org/W2132331020","https://openalex.org/W2149932816","https://openalex.org/W2163696969","https://openalex.org/W2165820775","https://openalex.org/W2912292072","https://openalex.org/W3010182501","https://openalex.org/W4294555155","https://openalex.org/W4301808069","https://openalex.org/W6996888795","https://openalex.org/W7046420581"],"related_works":["https://openalex.org/W4297923607","https://openalex.org/W2341851659","https://openalex.org/W2963029392","https://openalex.org/W2793442860","https://openalex.org/W2763916671","https://openalex.org/W1851760673","https://openalex.org/W2053402117","https://openalex.org/W2052987729","https://openalex.org/W1525594430","https://openalex.org/W2257350772"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}