{"id":"https://openalex.org/W1801713495","doi":"https://doi.org/10.1007/978-3-642-24364-6_9","title":"Superposition Modulo Non-linear Arithmetic","display_name":"Superposition Modulo Non-linear Arithmetic","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1801713495","doi":"https://doi.org/10.1007/978-3-642-24364-6_9","mag":"1801713495"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-24364-6_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-24364-6_9","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/A5027022102","display_name":"Andreas Eggers","orcid":null},"institutions":[{"id":"https://openalex.org/I129877168","display_name":"Carl von Ossietzky Universit\u00e4t Oldenburg","ror":"https://ror.org/033n9gh91","country_code":"DE","type":"education","lineage":["https://openalex.org/I129877168"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Andreas Eggers","raw_affiliation_strings":["Dept. of Computing Science, Carl von Ossietzky Universit\u00e4t Oldenburg, D-26111, Oldenburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Computing Science, Carl von Ossietzky Universit\u00e4t Oldenburg, D-26111, Oldenburg, Germany","institution_ids":["https://openalex.org/I129877168"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041988691","display_name":"Evgeny Kruglov","orcid":null},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]},{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Evgeny Kruglov","raw_affiliation_strings":["Universit\u00e4t des Saarlandes, Max-Planck-Institut f\u00fcr Informatik, Campus E1 4, D-66123, Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t des Saarlandes, Max-Planck-Institut f\u00fcr Informatik, Campus E1 4, D-66123, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712","https://openalex.org/I91712215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025670978","display_name":"Stefan Kupferschmid","orcid":null},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Stefan Kupferschmid","raw_affiliation_strings":["Institute of Computer Science, Albert-Ludwigs-University, D-79110, Freiburg im Breisgau, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Albert-Ludwigs-University, D-79110, Freiburg im Breisgau, Germany","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006930111","display_name":"Karsten Scheibler","orcid":null},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Karsten Scheibler","raw_affiliation_strings":["Institute of Computer Science, Albert-Ludwigs-University, D-79110, Freiburg im Breisgau, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Albert-Ludwigs-University, D-79110, Freiburg im Breisgau, Germany","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002477196","display_name":"Tino Teige","orcid":null},"institutions":[{"id":"https://openalex.org/I129877168","display_name":"Carl von Ossietzky Universit\u00e4t Oldenburg","ror":"https://ror.org/033n9gh91","country_code":"DE","type":"education","lineage":["https://openalex.org/I129877168"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tino Teige","raw_affiliation_strings":["Dept. of Computing Science, Carl von Ossietzky Universit\u00e4t Oldenburg, D-26111, Oldenburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Computing Science, Carl von Ossietzky Universit\u00e4t Oldenburg, D-26111, Oldenburg, Germany","institution_ids":["https://openalex.org/I129877168"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046034681","display_name":"Christoph Weidenbach","orcid":"https://orcid.org/0000-0001-6002-0458"},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]},{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christoph Weidenbach","raw_affiliation_strings":["Universit\u00e4t des Saarlandes, Max-Planck-Institut f\u00fcr Informatik, Campus E1 4, D-66123, Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t des Saarlandes, Max-Planck-Institut f\u00fcr Informatik, Campus E1 4, D-66123, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712","https://openalex.org/I91712215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":2.3192,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.88078431,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"119","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9986000061035156,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9986000061035156,"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":0.9972000122070312,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9968000054359436,"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/modulo","display_name":"Modulo","score":0.8673396110534668},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.7109742760658264},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6540881395339966},{"id":"https://openalex.org/keywords/superposition-principle","display_name":"Superposition principle","score":0.6422821879386902},{"id":"https://openalex.org/keywords/modulo-operation","display_name":"Modulo operation","score":0.6169288158416748},{"id":"https://openalex.org/keywords/saturation-arithmetic","display_name":"Saturation arithmetic","score":0.4389806091785431},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3686760365962982},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2553534507751465},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.19248953461647034},{"id":"https://openalex.org/keywords/arbitrary-precision-arithmetic","display_name":"Arbitrary-precision arithmetic","score":0.19101345539093018},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0625036358833313}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.8673396110534668},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.7109742760658264},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6540881395339966},{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.6422821879386902},{"id":"https://openalex.org/C183448482","wikidata":"https://www.wikidata.org/wiki/Q1799665","display_name":"Modulo operation","level":2,"score":0.6169288158416748},{"id":"https://openalex.org/C182775192","wikidata":"https://www.wikidata.org/wiki/Q913725","display_name":"Saturation arithmetic","level":3,"score":0.4389806091785431},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3686760365962982},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2553534507751465},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.19248953461647034},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.19101345539093018},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0625036358833313}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-642-24364-6_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-24364-6_9","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"},{"id":"pmh:oai:escidoc.org:escidoc:2047837","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-001A-1529-9","pdf_url":null,"source":{"id":"https://openalex.org/S7407052962","display_name":"Max Planck Digital Library","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"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":32,"referenced_works":["https://openalex.org/W47957325","https://openalex.org/W634866496","https://openalex.org/W1480909796","https://openalex.org/W1481397690","https://openalex.org/W1509261266","https://openalex.org/W1511963917","https://openalex.org/W1519551513","https://openalex.org/W1522448884","https://openalex.org/W1550776561","https://openalex.org/W1556566737","https://openalex.org/W1564749156","https://openalex.org/W1586677474","https://openalex.org/W1595962583","https://openalex.org/W1604594753","https://openalex.org/W1606555018","https://openalex.org/W1609596465","https://openalex.org/W1801713495","https://openalex.org/W1966647497","https://openalex.org/W1986264093","https://openalex.org/W2015287249","https://openalex.org/W2052434414","https://openalex.org/W2057361103","https://openalex.org/W2062897452","https://openalex.org/W2121280877","https://openalex.org/W2130519480","https://openalex.org/W2135185226","https://openalex.org/W2154128151","https://openalex.org/W2158859403","https://openalex.org/W2163850966","https://openalex.org/W2798401172","https://openalex.org/W3148608205","https://openalex.org/W4242363511"],"related_works":["https://openalex.org/W126207292","https://openalex.org/W2070252991","https://openalex.org/W2096889687","https://openalex.org/W1506998470","https://openalex.org/W2070522125","https://openalex.org/W1981011893","https://openalex.org/W2039921003","https://openalex.org/W631588072","https://openalex.org/W1509816403","https://openalex.org/W1577654796"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}