{"id":"https://openalex.org/W7140325576","doi":"https://doi.org/10.48550/arxiv.2603.22877","title":"Continuous Optimization for Satisfiability Modulo Theories on Linear Real Arithmetic","display_name":"Continuous Optimization for Satisfiability Modulo Theories on Linear Real Arithmetic","publication_year":2026,"publication_date":"2026-03-24","ids":{"openalex":"https://openalex.org/W7140325576","doi":"https://doi.org/10.48550/arxiv.2603.22877"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.22877","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22877","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.22877","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034264160","display_name":"Yunuo Cen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cen, Yunuo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062770200","display_name":"Daniel Ebler","orcid":"https://orcid.org/0000-0003-2696-8354"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ebler, Daniel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5085588788","display_name":"Xuanyao Fong","orcid":"https://orcid.org/0000-0001-5939-7389"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fong, Xuanyao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.671500027179718,"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":0.671500027179718,"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/T10904","display_name":"Embedded Systems Design Techniques","score":0.07150000333786011,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.057999998331069946,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.5782999992370605},{"id":"https://openalex.org/keywords/satisfiability-modulo-theories","display_name":"Satisfiability modulo theories","score":0.5774000287055969},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.5332000255584717},{"id":"https://openalex.org/keywords/soundness","display_name":"Soundness","score":0.5194000005722046},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.5085999965667725},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.4814000129699707},{"id":"https://openalex.org/keywords/binary-decision-diagram","display_name":"Binary decision diagram","score":0.4350000023841858},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.43149998784065247},{"id":"https://openalex.org/keywords/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.41690000891685486}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.5782999992370605},{"id":"https://openalex.org/C164155591","wikidata":"https://www.wikidata.org/wiki/Q2067766","display_name":"Satisfiability modulo theories","level":2,"score":0.5774000287055969},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.5332000255584717},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.5194000005722046},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.5085999965667725},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.4814000129699707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47540000081062317},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43540000915527344},{"id":"https://openalex.org/C3309909","wikidata":"https://www.wikidata.org/wiki/Q864155","display_name":"Binary decision diagram","level":2,"score":0.4350000023841858},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.43149998784065247},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42419999837875366},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.41690000891685486},{"id":"https://openalex.org/C148047603","wikidata":"https://www.wikidata.org/wiki/Q1014612","display_name":"Parallelizable manifold","level":2,"score":0.4058000147342682},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3901999890804291},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39010000228881836},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3804999887943268},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.35839998722076416},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.3440999984741211},{"id":"https://openalex.org/C92995354","wikidata":"https://www.wikidata.org/wiki/Q5165499","display_name":"Continuous optimization","level":4,"score":0.33390000462532043},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.31779998540878296},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.3046000003814697},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.2879999876022339},{"id":"https://openalex.org/C32029473","wikidata":"https://www.wikidata.org/wiki/Q7292010","display_name":"Randomized rounding","level":3,"score":0.28619998693466187},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2824999988079071},{"id":"https://openalex.org/C145671259","wikidata":"https://www.wikidata.org/wiki/Q1493786","display_name":"Discrete optimization","level":3,"score":0.28220000863075256},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.2687999904155731},{"id":"https://openalex.org/C2983394010","wikidata":"https://www.wikidata.org/wiki/Q19885330","display_name":"Continuous variable","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.26030001044273376}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.22877","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22877","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.22877","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22877","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Efficient":[0],"solutions":[1],"for":[2,53,81,149,178,205],"satisfiability":[3],"modulo":[4],"theories":[5],"(SMT)":[6],"are":[7,21],"integral":[8],"in":[9],"industrial":[10],"applications":[11],"such":[12],"as":[13,44],"hardware":[14],"verification":[15],"and":[16,34,47,116,165,181,189],"design":[17],"automation.":[18],"Existing":[19],"approaches":[20],"predominantly":[22],"based":[23],"on":[24],"conflict-driven":[25],"clause":[26],"learning,":[27],"which":[28,74],"is":[29,138,161,176],"structurally":[30],"difficult":[31],"to":[32,69,92,122,140,163,186,196],"parallelize":[33],"therefore":[35],"scales":[36],"poorly.":[37],"In":[38],"this":[39],"work,":[40],"we":[41,108],"introduce":[42],"FourierSMT":[43],"a":[45,70],"scalable":[46],"highly":[48],"parallelizable":[49],"continuous-variable":[50],"optimization":[51,207],"framework":[52,175],"SMT.":[54,82],"We":[55,124,155],"generalize":[56],"the":[57,66,76,85,103,110,118,129,141,145,153,158,169,172,203],"Walsh-Fourier":[58],"expansion":[59],"(WFE),":[60],"called":[61],"extended":[62,111],"WFE":[63],"(xWFE),":[64],"from":[65,120],"Boolean":[67],"domain":[68],"mixed":[71],"Boolean-real":[72],"domain,":[73],"allows":[75,148],"use":[77],"of":[78,87,98,106,133,144,152,171,208],"gradient":[79],"methods":[80],"This":[83,147],"addresses":[84],"challenge":[86],"finding":[88],"satisfying":[89],"variable":[90],"assignments":[91],"high-arity":[93],"constraints":[94,119],"by":[95],"local":[96],"updates":[97],"discrete":[99],"variables.":[100],"To":[101],"reduce":[102],"evaluation":[104],"complexity":[105],"xWFE,":[107],"present":[109],"binary":[112],"decision":[113],"diagram":[114],"(xBDD)":[115],"map":[117],"xWFE":[121],"xBDDs.":[123],"then":[125],"show":[126,156],"that":[127,157],"sampling":[128],"circuit-output":[130],"probability":[131],"(COP)":[132],"xBDDs":[134],"under":[135],"randomized":[136],"rounding":[137],"equivalent":[139],"expectation":[142],"value":[143],"xWFEs.":[146],"efficient":[150],"computation":[151],"constraints.":[154],"reduced":[159],"problem":[160],"guaranteed":[162],"converge":[164],"preserves":[166],"satisfiability,":[167],"ensuring":[168],"soundness":[170],"solutions.":[173],"The":[174],"benchmarked":[177],"large-scale":[179],"scheduling":[180],"placement":[182],"problems":[183],"with":[184,210],"up":[185],"10,000":[187],"variables":[188],"700,000":[190],"constraints,":[191],"achieving":[192],"8-fold":[193],"speedups":[194],"compared":[195],"state-of-the-art":[197],"SMT":[198],"solvers.":[199],"These":[200],"results":[201],"pave":[202],"way":[204],"GPU-based":[206],"SMTs":[209],"continuous":[211],"systems.":[212]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-26T00:00:00"}