{"id":"https://openalex.org/W1977456312","doi":"https://doi.org/10.1007/s10703-015-0228-1","title":"Under-approximating loops in C programs for fast counterexample detection","display_name":"Under-approximating loops in C programs for fast counterexample detection","publication_year":2015,"publication_date":"2015-04-16","ids":{"openalex":"https://openalex.org/W1977456312","doi":"https://doi.org/10.1007/s10703-015-0228-1","mag":"1977456312","pmid":"https://pubmed.ncbi.nlm.nih.gov/26900259"},"language":"en","primary_location":{"id":"doi:10.1007/s10703-015-0228-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10703-015-0228-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10703-015-0228-1.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","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10703-015-0228-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086206346","display_name":"Daniel Kroening","orcid":"https://orcid.org/0000-0002-6681-5283"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Daniel Kroening","raw_affiliation_strings":["University of Oxford, Oxford, UK","University of Oxford , Oxford , UK"],"affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"University of Oxford , Oxford , UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047259577","display_name":"Matt Lewis","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Matt Lewis","raw_affiliation_strings":["University of Oxford, Oxford, UK","University of Oxford , Oxford , UK"],"affiliations":[{"raw_affiliation_string":"University of Oxford, Oxford, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"University of Oxford , Oxford , UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017958562","display_name":"Georg Wei\u00dfenbacher","orcid":"https://orcid.org/0000-0002-0143-632X"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Georg Weissenbacher","raw_affiliation_strings":["Vienna University of Technology, Vienna, Austria","Vienna University of technology, Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Vienna University of Technology, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Vienna University of technology, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5086206346"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":{"value":2690,"currency":"EUR","value_usd":3490},"apc_paid":{"value":2690,"currency":"EUR","value_usd":3490},"fwci":2.183,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.87882781,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"47","issue":"1","first_page":"75","last_page":"92"},"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/T11424","display_name":"Security and Verification in Computing","score":0.9983999729156494,"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/T10743","display_name":"Software Testing and Debugging Techniques","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/counterexample","display_name":"Counterexample","score":0.9577611684799194},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6528135538101196},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.6396923065185547},{"id":"https://openalex.org/keywords/abstraction","display_name":"Abstraction","score":0.62114417552948},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.6198021173477173},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6009126305580139},{"id":"https://openalex.org/keywords/loop","display_name":"Loop (graph theory)","score":0.5865921974182129},{"id":"https://openalex.org/keywords/model-checking","display_name":"Model checking","score":0.4972231686115265},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.465831458568573},{"id":"https://openalex.org/keywords/predicate-abstraction","display_name":"Predicate abstraction","score":0.43737781047821045},{"id":"https://openalex.org/keywords/for-loop","display_name":"For loop","score":0.43463167548179626},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40555310249328613},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3596500754356384},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22301942110061646},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.18951448798179626},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.18734383583068848},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.09614616632461548},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07928627729415894}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.9577611684799194},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6528135538101196},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.6396923065185547},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.62114417552948},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.6198021173477173},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6009126305580139},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.5865921974182129},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.4972231686115265},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.465831458568573},{"id":"https://openalex.org/C2779907942","wikidata":"https://www.wikidata.org/wiki/Q7239630","display_name":"Predicate abstraction","level":3,"score":0.43737781047821045},{"id":"https://openalex.org/C2779624466","wikidata":"https://www.wikidata.org/wiki/Q838119","display_name":"For loop","level":3,"score":0.43463167548179626},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40555310249328613},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3596500754356384},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22301942110061646},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.18951448798179626},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.18734383583068848},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.09614616632461548},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07928627729415894},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10703-015-0228-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10703-015-0228-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10703-015-0228-1.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":"pmid:26900259","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26900259","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formal methods in system design","raw_type":null},{"id":"pmh:oai:europepmc.org:3730175","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/4750468","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"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":null,"raw_type":"Text"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:28831064-29d6-4edd-b689-df8069b440c6","is_oa":true,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:28831064-29d6-4edd-b689-df8069b440c6","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"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":"","raw_type":"Journal article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:44bfe75f-6d20-4960-b7ad-29eac0c31556","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:44bfe75f-6d20-4960-b7ad-29eac0c31556","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference item"}],"best_oa_location":{"id":"doi:10.1007/s10703-015-0228-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10703-015-0228-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10703-015-0228-1.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":[{"score":0.7799999713897705,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1934935867","display_name":null,"funder_award_id":"Engineering and Physical Sciences R","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2512157488","display_name":null,"funder_award_id":"VRG11-005","funder_id":"https://openalex.org/F4320321003","funder_display_name":"Vienna Science and Technology Fund"},{"id":"https://openalex.org/G2598114656","display_name":null,"funder_award_id":"H017585/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2602268313","display_name":"Verification of Shared-Memory Concurrent Software","funder_award_id":"EP/H017585/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6941323120","display_name":null,"funder_award_id":"EP/H017585/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6947071278","display_name":null,"funder_award_id":"S11403","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7052333967","display_name":null,"funder_award_id":"S11403-N23","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321003","display_name":"Vienna Science and Technology Fund","ror":"https://ror.org/01f9mc681"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1977456312.pdf","grobid_xml":"https://content.openalex.org/works/W1977456312.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1491355701","https://openalex.org/W1503677488","https://openalex.org/W1515621470","https://openalex.org/W1531054827","https://openalex.org/W1546153726","https://openalex.org/W1547584984","https://openalex.org/W1565898282","https://openalex.org/W1584436405","https://openalex.org/W1597840949","https://openalex.org/W1600009974","https://openalex.org/W1848981483","https://openalex.org/W1968428133","https://openalex.org/W1987289444","https://openalex.org/W2024978854","https://openalex.org/W2030865387","https://openalex.org/W2037929850","https://openalex.org/W2049707975","https://openalex.org/W2105357036","https://openalex.org/W2118362509","https://openalex.org/W2129538349","https://openalex.org/W2294635730","https://openalex.org/W2295903414","https://openalex.org/W2611153783","https://openalex.org/W2911612809","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4308502799","https://openalex.org/W4361986567","https://openalex.org/W2006786376","https://openalex.org/W2949974473","https://openalex.org/W1967993207","https://openalex.org/W2953113086","https://openalex.org/W1552191998","https://openalex.org/W2056825861","https://openalex.org/W2218365969","https://openalex.org/W1977456312"],"abstract_inverted_index":{"Many":[0],"software":[1],"model":[2,137],"checkers":[3],"only":[4],"detect":[5,156],"counterexamples":[6,158],"with":[7,70,121,132],"deep":[8,157],"loops":[9],"after":[10],"exploring":[11],"numerous":[12],"spurious":[13],"and":[14,83,135,139],"increasingly":[15],"longer":[16],"counterexamples.":[17],"We":[18,128],"propose":[19],"a":[20,37,94,122,145],"technique":[21],"that":[22,32,162],"aims":[23],"at":[24],"eliminating":[25],"this":[26],"weakness":[27],"by":[28],"constructing":[29],"auxiliary":[30,55],"paths":[31,56],"represent":[33],"the":[34,46,59,62,66,73,88,101,141],"effect":[35,48],"of":[36,39,49,61,76,125,147],"range":[38,124],"loop":[40,52,89],"iterations.":[41],"Unlike":[42],"acceleration,":[43],"which":[44],"captures":[45],"exact":[47],"arbitrarily":[50],"many":[51],"iterations,":[53],"these":[54],"may":[57,92],"under-approximate":[58],"behaviour":[60],"loops.":[63],"In":[64],"return,":[65],"approximation":[67],"is":[68],"sound":[69],"respect":[71],"to":[72,85,154],"bit-vector":[74],"semantics":[75],"programs.":[77],"Our":[78],"approach":[79],"supports":[80],"arbitrary":[81],"conditions":[82],"assignments":[84],"arrays":[86],"in":[87,159],"body,":[90],"but":[91],"as":[93],"result":[95],"introduce":[96],"quantified":[97],"conditionals.":[98],"To":[99],"reduce":[100],"resulting":[102,142],"performance":[103],"penalty,":[104],"we":[105],"present":[106],"two":[107],"quantifier":[108],"elimination":[109],"techniques":[110,131],"specially":[111],"geared":[112],"towards":[113],"our":[114,130],"application.":[115],"Loop":[116],"under-approximation":[117],"can":[118],"be":[119],"combined":[120],"broad":[123],"verification":[126],"techniques.":[127],"paired":[129],"lazy":[133],"abstraction":[134],"bounded":[136],"checking,":[138],"evaluated":[140],"tool":[143],"on":[144],"number":[146],"buffer":[148],"overflow":[149],"benchmarks,":[150],"demonstrating":[151],"its":[152],"ability":[153],"efficiently":[155],"C":[160],"programs":[161],"manipulate":[163],"arrays.":[164]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}