{"id":"https://openalex.org/W4415903173","doi":"https://doi.org/10.24963/kr.2025/53","title":"Efficient Volume Computation for SMT Formulas","display_name":"Efficient Volume Computation for SMT Formulas","publication_year":2025,"publication_date":"2025-11-01","ids":{"openalex":"https://openalex.org/W4415903173","doi":"https://doi.org/10.24963/kr.2025/53"},"language":null,"primary_location":{"id":"doi:10.24963/kr.2025/53","is_oa":true,"landing_page_url":"https://doi.org/10.24963/kr.2025/53","pdf_url":"https://proceedings.kr.org/2025/53/kr2025-0053-shaw-et-al.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the TwentySecond International Conference on Principles of Knowledge Representation and Reasoning","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://proceedings.kr.org/2025/53/kr2025-0053-shaw-et-al.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111097761","display_name":"Arijit Shaw","orcid":null},"institutions":[{"id":"https://openalex.org/I19149307","display_name":"Chennai Mathematical Institute","ror":"https://ror.org/04zp24820","country_code":"IN","type":"education","lineage":["https://openalex.org/I19149307"]},{"id":"https://openalex.org/I4210102982","display_name":"Centre for Research in Engineering Surface Technology","ror":"https://ror.org/018q3fa22","country_code":"IE","type":"other","lineage":["https://openalex.org/I4210102982"]}],"countries":["IE","IN"],"is_corresponding":true,"raw_author_name":"Arijit Shaw","raw_affiliation_strings":["Chennai Mathematical Institute","IAI, TCG CREST, Kolkata"],"affiliations":[{"raw_affiliation_string":"Chennai Mathematical Institute","institution_ids":["https://openalex.org/I19149307"]},{"raw_affiliation_string":"IAI, TCG CREST, Kolkata","institution_ids":["https://openalex.org/I4210102982"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120259910","display_name":"Uddalok Sarkar","orcid":null},"institutions":[{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Uddalok Sarkar","raw_affiliation_strings":["Indian Statistical Institute, Kolkata"],"affiliations":[{"raw_affiliation_string":"Indian Statistical Institute, Kolkata","institution_ids":["https://openalex.org/I6498739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041528950","display_name":"Kuldeep S. Meel","orcid":"https://orcid.org/0000-0001-9423-5270"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]},{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Kuldeep S. Meel","raw_affiliation_strings":["Georgia Institute of Technology","University of Toronto"],"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"University of Toronto","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5111097761"],"corresponding_institution_ids":["https://openalex.org/I19149307","https://openalex.org/I4210102982"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.32687016,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"544","last_page":"554"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.7120000123977661,"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":0.7120000123977661,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.1648000031709671,"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"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.026399999856948853,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/satisfiability-modulo-theories","display_name":"Satisfiability modulo theories","score":0.7954000234603882},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5285999774932861},{"id":"https://openalex.org/keywords/volume","display_name":"Volume (thermodynamics)","score":0.5239999890327454},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.5220000147819519},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5110999941825867},{"id":"https://openalex.org/keywords/automated-reasoning","display_name":"Automated reasoning","score":0.5052000284194946},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49459999799728394},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.42579999566078186},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.3901999890804291},{"id":"https://openalex.org/keywords/semiring","display_name":"Semiring","score":0.3896999955177307}],"concepts":[{"id":"https://openalex.org/C164155591","wikidata":"https://www.wikidata.org/wiki/Q2067766","display_name":"Satisfiability modulo theories","level":2,"score":0.7954000234603882},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6086000204086304},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5285999774932861},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.5239999890327454},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.5220000147819519},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5110999941825867},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5092999935150146},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.5052000284194946},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49459999799728394},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.49309998750686646},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.42579999566078186},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.3901999890804291},{"id":"https://openalex.org/C21696900","wikidata":"https://www.wikidata.org/wiki/Q1333055","display_name":"Semiring","level":2,"score":0.3896999955177307},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.3765000104904175},{"id":"https://openalex.org/C2777168461","wikidata":"https://www.wikidata.org/wiki/Q42196253","display_name":"Set operations","level":3,"score":0.36719998717308044},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.35899999737739563},{"id":"https://openalex.org/C200415742","wikidata":"https://www.wikidata.org/wiki/Q1350285","display_name":"True quantified Boolean formula","level":2,"score":0.3368000090122223},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.335099995136261},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3312999904155731},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31630000472068787},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.31619998812675476},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.3124000132083893},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.2939999997615814},{"id":"https://openalex.org/C33054407","wikidata":"https://www.wikidata.org/wiki/Q6504747","display_name":"Software verification","level":5,"score":0.2874999940395355},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.28540000319480896},{"id":"https://openalex.org/C7342684","wikidata":"https://www.wikidata.org/wiki/Q520777","display_name":"Boolean data type","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C16221470","wikidata":"https://www.wikidata.org/wiki/Q846564","display_name":"Conjunctive normal form","level":2,"score":0.2630999982357025}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.24963/kr.2025/53","is_oa":true,"landing_page_url":"https://doi.org/10.24963/kr.2025/53","pdf_url":"https://proceedings.kr.org/2025/53/kr2025-0053-shaw-et-al.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the TwentySecond International Conference on Principles of Knowledge Representation and Reasoning","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.24963/kr.2025/53","is_oa":true,"landing_page_url":"https://doi.org/10.24963/kr.2025/53","pdf_url":"https://proceedings.kr.org/2025/53/kr2025-0053-shaw-et-al.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the TwentySecond International Conference on Principles of Knowledge Representation and Reasoning","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1364794008","display_name":null,"funder_award_id":"RGPIN-2024-05956","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G1597412403","display_name":null,"funder_award_id":"RGPIN-","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G6221715925","display_name":null,"funder_award_id":"RGPIN","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G8105784103","display_name":null,"funder_award_id":"RGPIN-202","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G8284766523","display_name":null,"funder_award_id":"(NSERC)","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320312716","display_name":"Innovation, Science and Economic Development Canada","ror":"https://ror.org/03zp01h17"},{"id":"https://openalex.org/F4320322015","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087"},{"id":"https://openalex.org/F4320331257","display_name":"Alliance de recherche num\u00e9rique du Canada","ror":"https://ror.org/010r6td27"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415903173.pdf","grobid_xml":"https://content.openalex.org/works/W4415903173.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Satisfiability":[0],"Modulo":[1],"Theory":[2],"(SMT)":[3],"has":[4],"recently":[5],"emerged":[6],"as":[7],"a":[8,95,126],"powerful":[9],"tool":[10],"for":[11],"solving":[12,80],"various":[13],"automated":[14],"reasoning":[15],"problems":[16],"across":[17],"diverse":[18],"domains.":[19],"Unlike":[20],"traditional":[21],"satisfiability":[22],"methods":[23],"confined":[24],"to":[25,46,93,110],"Boolean":[26],"variables,":[27],"SMT":[28,55,73,108,120],"can":[29],"reason":[30],"on":[31,143],"real-life":[32],"variables":[33],"like":[34],"bitvectors,":[35],"integers,":[36],"and":[37,90,136,153],"reals.":[38],"A":[39],"natural":[40],"extension":[41],"in":[42,53,79,85,146],"this":[43],"context":[44],"is":[45,62,77],"ask":[47],"quantitative":[48,82],"questions.":[49],"One":[50],"such":[51],"query":[52],"the":[54,64,67,105,116],"theory":[56],"of":[57,66,107,119,128],"Linear":[58,121],"Real":[59,122],"Arithmetic":[60,123],"(LRA)":[61],"computing":[63],"volume":[65,111,150],"entire":[68],"satisfiable":[69],"region":[70],"defined":[71],"by":[72],"formulas.":[74],"This":[75],"problem":[76],"important":[78],"different":[81],"verification":[83],"queries":[84],"software":[86],"verification,":[87],"cyber-physical":[88],"systems,":[89],"neural":[91],"networks,":[92],"mention":[94],"few.":[96],"We":[97],"introduce":[98],"ttc,":[99],"an":[100],"efficient":[101],"algorithm":[102,141],"that":[103],"extends":[104],"capabilities":[106],"solvers":[109],"computation.":[112],"Our":[113,140],"method":[114],"decomposes":[115],"solution":[117],"space":[118],"formulas":[124],"into":[125],"union":[127],"overlapping":[129],"convex":[130],"polytopes,":[131],"then":[132],"computes":[133],"their":[134,138],"volumes":[135],"calculates":[137],"union.":[139],"builds":[142],"recent":[144],"developments":[145],"streaming-mode":[147],"set":[148],"unions,":[149],"computation":[151],"algorithms,":[152],"AllSAT":[154],"techniques.":[155],"Experimental":[156],"evaluations":[157],"demonstrate":[158],"significant":[159],"performance":[160],"improvements":[161],"over":[162],"existing":[163],"state-of-the-art":[164],"approaches.":[165]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-11-05T00:00:00"}