{"id":"https://openalex.org/W2898484043","doi":"https://doi.org/10.1007/s10817-018-9490-4","title":"Formally Verifying the Solution to the Boolean Pythagorean Triples Problem","display_name":"Formally Verifying the Solution to the Boolean Pythagorean Triples Problem","publication_year":2018,"publication_date":"2018-10-27","ids":{"openalex":"https://openalex.org/W2898484043","doi":"https://doi.org/10.1007/s10817-018-9490-4","mag":"2898484043"},"language":"en","primary_location":{"id":"doi:10.1007/s10817-018-9490-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10817-018-9490-4","pdf_url":null,"source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","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/A5082561369","display_name":"Lu\u0131\u0301s Cruz-Filipe","orcid":"https://orcid.org/0000-0002-7866-7484"},"institutions":[{"id":"https://openalex.org/I177969490","display_name":"University of Southern Denmark","ror":"https://ror.org/03yrrjy16","country_code":"DK","type":"education","lineage":["https://openalex.org/I177969490"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Lu\u00eds Cruz-Filipe","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230, Odense M, Denmark"],"raw_orcid":"https://orcid.org/0000-0002-7866-7484","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230, Odense M, Denmark","institution_ids":["https://openalex.org/I177969490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002246957","display_name":"Jo\u00e3o Marques\u2010Silva","orcid":"https://orcid.org/0000-0002-6632-3086"},"institutions":[{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Joao Marques-Silva","raw_affiliation_strings":["LaSIGE, Faculty of Science, University of Lisbon, Lisbon, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LaSIGE, Faculty of Science, University of Lisbon, Lisbon, Portugal","institution_ids":["https://openalex.org/I141596103"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058200123","display_name":"Peter Schneider\u2013Kamp","orcid":"https://orcid.org/0000-0003-4000-5570"},"institutions":[{"id":"https://openalex.org/I177969490","display_name":"University of Southern Denmark","ror":"https://ror.org/03yrrjy16","country_code":"DK","type":"education","lineage":["https://openalex.org/I177969490"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Peter Schneider-Kamp","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230, Odense M, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230, Odense M, Denmark","institution_ids":["https://openalex.org/I177969490"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082561369"],"corresponding_institution_ids":["https://openalex.org/I177969490"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.3104,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.85644771,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"63","issue":"3","first_page":"695","last_page":"722"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9990000128746033,"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":0.9990000128746033,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9828000068664551,"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/T12504","display_name":"Mathematics and Applications","score":0.9689000248908997,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pythagorean-triple","display_name":"Pythagorean triple","score":0.7791405320167542},{"id":"https://openalex.org/keywords/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.48696693778038025},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4574841558933258},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4464320242404938},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3537638783454895},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.33663126826286316},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12455731630325317}],"concepts":[{"id":"https://openalex.org/C80918210","wikidata":"https://www.wikidata.org/wiki/Q208225","display_name":"Pythagorean triple","level":3,"score":0.7791405320167542},{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.48696693778038025},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4574841558933258},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4464320242404938},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3537638783454895},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33663126826286316},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12455731630325317},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10817-018-9490-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10817-018-9490-4","pdf_url":null,"source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","raw_type":"journal-article"},{"id":"pmh:oai:sdu.dk:openaire_cris_publications/65480451-893c-46ab-8200-1c64b1fc711c","is_oa":false,"landing_page_url":"https://portal.findresearcher.sdu.dk/da/publications/65480451-893c-46ab-8200-1c64b1fc711c","pdf_url":null,"source":{"id":"https://openalex.org/S4306400423","display_name":"University of Southern Denmark Research Portal (University of Southern Denmark)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177969490","host_organization_name":"University of Southern Denmark","host_organization_lineage":["https://openalex.org/I177969490"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cruz-Filipe, L, Marques-Silva, J & Schneider-Kamp, P 2019, 'Formally Verifying the Solution to the Boolean Pythagorean Triples Problem', Journal of Automated Reasoning, vol. 63, no. 3, pp. 695-722. https://doi.org/10.1007/s10817-018-9490-4","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1611354016","display_name":null,"funder_award_id":"DFF-7014-00041","funder_id":"https://openalex.org/F4320310485","funder_display_name":"Natur og Univers, Det Frie Forskningsr\u00e5d"}],"funders":[{"id":"https://openalex.org/F4320310485","display_name":"Natur og Univers, Det Frie Forskningsr\u00e5d","ror":"https://ror.org/03ge1nb22"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W27762129","https://openalex.org/W264897126","https://openalex.org/W1496529478","https://openalex.org/W1511662047","https://openalex.org/W1522720500","https://openalex.org/W1553511155","https://openalex.org/W1656268799","https://openalex.org/W1807519183","https://openalex.org/W1830871583","https://openalex.org/W1986402635","https://openalex.org/W2003992820","https://openalex.org/W2023035194","https://openalex.org/W2036265926","https://openalex.org/W2057361103","https://openalex.org/W2090857454","https://openalex.org/W2117247884","https://openalex.org/W2145199041","https://openalex.org/W2153839473","https://openalex.org/W2345876752","https://openalex.org/W2543800696","https://openalex.org/W2564212270","https://openalex.org/W2584482282","https://openalex.org/W2734612968","https://openalex.org/W2735855164","https://openalex.org/W2741154258","https://openalex.org/W2741979441","https://openalex.org/W2888067689","https://openalex.org/W2949670469","https://openalex.org/W3023731641","https://openalex.org/W3104269339","https://openalex.org/W3144847833"],"related_works":["https://openalex.org/W3038906685","https://openalex.org/W2392975301","https://openalex.org/W2259363500","https://openalex.org/W2387543012","https://openalex.org/W2620974800","https://openalex.org/W2790200812","https://openalex.org/W2368479431","https://openalex.org/W4280581009","https://openalex.org/W4287077343","https://openalex.org/W3182949439"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}