{"id":"https://openalex.org/W2613671682","doi":"https://doi.org/10.1007/s10703-017-0278-7","title":"New techniques for linear arithmetic: cubes and equalities","display_name":"New techniques for linear arithmetic: cubes and equalities","publication_year":2017,"publication_date":"2017-05-08","ids":{"openalex":"https://openalex.org/W2613671682","doi":"https://doi.org/10.1007/s10703-017-0278-7","mag":"2613671682"},"language":"en","primary_location":{"id":"doi:10.1007/s10703-017-0278-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10703-017-0278-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10703-017-0278-7.pdf","source":{"id":"https://openalex.org/S3845260","display_name":"Formal Methods in System Design","issn_l":"0925-9856","issn":["0925-9856","1572-8102"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formal Methods in System Design","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10703-017-0278-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069366068","display_name":"Martin Bromberger","orcid":"https://orcid.org/0000-0001-7256-2190"},"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":true,"raw_author_name":"Martin Bromberger","raw_affiliation_strings":["Graduate School of Computer Science, Saarland Informatics, Campus E1 3, 66123, Saarbr\u00fccken, Germany","Max-Planck-Institut f\u00fcr Informatik, Saarland Informatics, Campus E1 4, 66123, Saarbr\u00fccken, Germany","VERIDIS - Modeling and Verification of Distributed Algorithms and Systems (France)","Saarbr\u00fccken Graduate School of Computer Science (Germany)"],"raw_orcid":"https://orcid.org/0000-0001-7256-2190","affiliations":[{"raw_affiliation_string":"Graduate School of Computer Science, Saarland Informatics, Campus E1 3, 66123, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712","https://openalex.org/I91712215"]},{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Informatik, Saarland Informatics, Campus E1 4, 66123, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]},{"raw_affiliation_string":"VERIDIS - Modeling and Verification of Distributed Algorithms and Systems (France)","institution_ids":[]},{"raw_affiliation_string":"Saarbr\u00fccken Graduate School of Computer Science (Germany)","institution_ids":[]}]},{"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"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christoph Weidenbach","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Informatik, Saarland Informatics, Campus E1 4, 66123, Saarbr\u00fccken, Germany","MPII - Max-Planck-Institut f\u00fcr Informatik (Campus E-1 4, 66123 Saarbr\u00fccken, Germany - Germany)","VERIDIS - Modeling and Verification of Distributed Algorithms and Systems (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Informatik, Saarland Informatics, Campus E1 4, 66123, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I4210109712"]},{"raw_affiliation_string":"MPII - Max-Planck-Institut f\u00fcr Informatik (Campus E-1 4, 66123 Saarbr\u00fccken, Germany - Germany)","institution_ids":["https://openalex.org/I4210109712"]},{"raw_affiliation_string":"VERIDIS - Modeling and Verification of Distributed Algorithms and Systems (France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069366068"],"corresponding_institution_ids":["https://openalex.org/I4210109712","https://openalex.org/I91712215"],"apc_list":{"value":2690,"currency":"EUR","value_usd":3490},"apc_paid":{"value":2690,"currency":"EUR","value_usd":3490},"fwci":1.6036,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.84843834,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"51","issue":"3","first_page":"433","last_page":"461"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9973000288009644,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9884999990463257,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.6117841005325317},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5724221467971802},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5309155583381653},{"id":"https://openalex.org/keywords/arbitrary-precision-arithmetic","display_name":"Arbitrary-precision arithmetic","score":0.5168150663375854},{"id":"https://openalex.org/keywords/linear-map","display_name":"Linear map","score":0.5120985507965088},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5020368099212646},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.49698808789253235},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.45073947310447693},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.43500852584838867},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36900436878204346},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3072027564048767},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09931150078773499}],"concepts":[{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.6117841005325317},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5724221467971802},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5309155583381653},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.5168150663375854},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.5120985507965088},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5020368099212646},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.49698808789253235},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.45073947310447693},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.43500852584838867},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36900436878204346},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3072027564048767},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09931150078773499},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10703-017-0278-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10703-017-0278-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10703-017-0278-7.pdf","source":{"id":"https://openalex.org/S3845260","display_name":"Formal Methods in System Design","issn_l":"0925-9856","issn":["0925-9856","1572-8102"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formal Methods in System Design","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01656397v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01656397","pdf_url":"https://inria.hal.science/hal-01656397v1/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formal Methods in System Design, 2017, 51 (3), pp.433-461. ⟨10.1007/s10703-017-0278-7⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.mpg.de:item_2496284","is_oa":true,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-002E-260E-C","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formal Methods in System Design","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10703-017-0278-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10703-017-0278-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10703-017-0278-7.pdf","source":{"id":"https://openalex.org/S3845260","display_name":"Formal Methods in System Design","issn_l":"0925-9856","issn":["0925-9856","1572-8102"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formal Methods in System Design","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322434","display_name":"Max-Planck-Gesellschaft","ror":"https://ror.org/01hhn8329"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2613671682.pdf","grobid_xml":"https://content.openalex.org/works/W2613671682.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W147487200","https://openalex.org/W221832247","https://openalex.org/W1480261666","https://openalex.org/W1480909796","https://openalex.org/W1545415851","https://openalex.org/W1553543780","https://openalex.org/W1851092725","https://openalex.org/W1857626577","https://openalex.org/W1963547452","https://openalex.org/W1982719520","https://openalex.org/W1996622306","https://openalex.org/W2013702670","https://openalex.org/W2013925092","https://openalex.org/W2019147273","https://openalex.org/W2097699872","https://openalex.org/W2103658959","https://openalex.org/W2119144375","https://openalex.org/W2124749403","https://openalex.org/W2125967324","https://openalex.org/W2126774253","https://openalex.org/W2167324057","https://openalex.org/W2188469581","https://openalex.org/W2276124093","https://openalex.org/W2296319761","https://openalex.org/W2491318681","https://openalex.org/W2496185699","https://openalex.org/W2556462024","https://openalex.org/W2611147814","https://openalex.org/W4246691913","https://openalex.org/W4250589301","https://openalex.org/W4285719527","https://openalex.org/W4299514408","https://openalex.org/W4301808069"],"related_works":["https://openalex.org/W2916710807","https://openalex.org/W2413588304","https://openalex.org/W2774705104","https://openalex.org/W4286907761","https://openalex.org/W2109307142","https://openalex.org/W4391021453","https://openalex.org/W2085911975","https://openalex.org/W2389228754","https://openalex.org/W3138373256","https://openalex.org/W1965191890"],"abstract_inverted_index":{"We":[0,139],"present":[1],"several":[2,135,194],"new":[3],"techniques":[4],"for":[5,59,72,91,173],"linear":[6,16,33,60,144,159,187,207],"arithmetic":[7,34,61,160,188,208],"constraint":[8],"solving.":[9],"They":[10],"are":[11,51,88,128],"all":[12,174,182],"based":[13,47],"on":[14,48,130],"the":[15,69,81,84,107,143,152,186,218],"cube":[17,145],"transformation,":[18],"a":[19,30,37,40,73,94,156,167,171,178,204,211],"method":[20,168],"presented":[21],"here,":[22],"which":[23],"allows":[24,199],"us":[25,200],"to":[26,79,134,150,201],"efficiently":[27],"determine":[28],"whether":[29,203],"system":[31,157,205],"of":[32,39,83,97,158,181,206,220,224],"constraints":[35,92,209],"contains":[36],"hypercube":[38],"given":[41,212],"edge":[42],"length.":[43],"Our":[44],"first":[45],"findings":[46],"this":[49,163],"transformation":[50,146],"two":[52],"sound":[53],"tests":[54,76,87,127],"that":[55,125,142,169],"find":[56],"integer":[57,98],"solutions":[58],"constraints.":[62,161,189],"While":[63],"many":[64],"complete":[65],"methods":[66],"search":[67],"along":[68],"problem":[70,116],"surface":[71],"solution,":[74],"these":[75,131],"use":[77],"cubes":[78],"explore":[80],"interior":[82],"problems.":[85],"The":[86,190],"especially":[89],"efficient":[90],"with":[93,102,118],"large":[95],"number":[96],"solutions,":[99],"e.g.,":[100],"those":[101],"infinite":[103,119],"lattice":[104,120],"width.":[105,121],"Inside":[106],"SMT-LIB":[108],"benchmarks,":[109],"we":[110,165],"have":[111],"found":[112],"almost":[113],"one":[114],"thousand":[115],"instances":[117,132],"Experimental":[122],"results":[123],"confirm":[124],"our":[126],"superior":[129],"compared":[133],"state-of-the-art":[136],"SMT":[137],"solvers.":[138],"also":[140],"discovered":[141],"can":[147],"be":[148],"used":[149],"investigate":[151],"equalities":[153,183],"implied":[154,175,184],"by":[155,185],"For":[162,196],"purpose,":[164],"developed":[166],"computes":[170],"basis":[172,192],"equalities,":[176],"i.e.,":[177],"finite":[179],"representation":[180],"equality":[191],"has":[193],"applications.":[195],"instance,":[197],"it":[198],"verify":[202],"implies":[210],"equality.":[213],"This":[214],"is":[215],"valuable":[216],"in":[217],"context":[219],"Nelson\u2013Oppen":[221],"style":[222],"combinations":[223],"theories.":[225]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}