{"id":"https://openalex.org/W2185676247","doi":"https://doi.org/10.1145/2837614.2837664","title":"Learning invariants using decision trees and implication counterexamples","display_name":"Learning invariants using decision trees and implication counterexamples","publication_year":2016,"publication_date":"2016-01-07","ids":{"openalex":"https://openalex.org/W2185676247","doi":"https://doi.org/10.1145/2837614.2837664","mag":"2185676247"},"language":"en","primary_location":{"id":"doi:10.1145/2837614.2837664","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2837614.2837664","pdf_url":"http://dl.acm.org/ft_gateway.cfm?id=2837664&type=pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://dl.acm.org/ft_gateway.cfm?id=2837664&type=pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025408312","display_name":"Pranav Garg","orcid":"https://orcid.org/0000-0002-0575-6320"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Pranav Garg","raw_affiliation_strings":["University of Illinois at Urbana-Champaign, USA"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064701353","display_name":"Daniel Neider","orcid":"https://orcid.org/0000-0001-9276-6342"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Neider","raw_affiliation_strings":["University of Illinois at Urbana-Champaign, USA"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112870293","display_name":"P. Madhusudan","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. Madhusudan","raw_affiliation_strings":["University of Illinois at Urbana-Champaign, USA"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023802054","display_name":"Dan Roth","orcid":"https://orcid.org/0009-0002-1447-5173"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dan Roth","raw_affiliation_strings":["University of Illinois at Urbana-Champaign, USA"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5025408312"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":34.0128,"has_fulltext":true,"cited_by_count":163,"citation_normalized_percentile":{"value":0.99684838,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"499","last_page":"512"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9993000030517578,"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/T10260","display_name":"Software Engineering Research","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T12535","display_name":"Machine Learning and Data Classification","score":0.994700014591217,"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/counterexample","display_name":"Counterexample","score":0.8189501166343689},{"id":"https://openalex.org/keywords/decision-tree","display_name":"Decision tree","score":0.6898438930511475},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6780722141265869},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.5865117311477661},{"id":"https://openalex.org/keywords/id3-algorithm","display_name":"ID3 algorithm","score":0.5698879361152649},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5648932456970215},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5545213222503662},{"id":"https://openalex.org/keywords/suite","display_name":"Suite","score":0.5542141199111938},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4994041919708252},{"id":"https://openalex.org/keywords/alternating-decision-tree","display_name":"Alternating decision tree","score":0.4935418367385864},{"id":"https://openalex.org/keywords/decision-tree-learning","display_name":"Decision tree learning","score":0.45842304825782776},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.44879311323165894},{"id":"https://openalex.org/keywords/algorithmic-learning-theory","display_name":"Algorithmic learning theory","score":0.4240514039993286},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3785708248615265},{"id":"https://openalex.org/keywords/active-learning","display_name":"Active learning (machine learning)","score":0.3405361771583557},{"id":"https://openalex.org/keywords/incremental-decision-tree","display_name":"Incremental decision tree","score":0.3394697904586792},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.18081018328666687},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.16791173815727234},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1301051676273346}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.8189501166343689},{"id":"https://openalex.org/C84525736","wikidata":"https://www.wikidata.org/wiki/Q831366","display_name":"Decision tree","level":2,"score":0.6898438930511475},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6780722141265869},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5865117311477661},{"id":"https://openalex.org/C183931066","wikidata":"https://www.wikidata.org/wiki/Q1653378","display_name":"ID3 algorithm","level":5,"score":0.5698879361152649},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5648932456970215},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5545213222503662},{"id":"https://openalex.org/C79581498","wikidata":"https://www.wikidata.org/wiki/Q1367530","display_name":"Suite","level":2,"score":0.5542141199111938},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4994041919708252},{"id":"https://openalex.org/C120136583","wikidata":"https://www.wikidata.org/wiki/Q4736414","display_name":"Alternating decision tree","level":5,"score":0.4935418367385864},{"id":"https://openalex.org/C5481197","wikidata":"https://www.wikidata.org/wiki/Q16766476","display_name":"Decision tree learning","level":3,"score":0.45842304825782776},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.44879311323165894},{"id":"https://openalex.org/C32254414","wikidata":"https://www.wikidata.org/wiki/Q4724364","display_name":"Algorithmic learning theory","level":3,"score":0.4240514039993286},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3785708248615265},{"id":"https://openalex.org/C77967617","wikidata":"https://www.wikidata.org/wiki/Q4677561","display_name":"Active learning (machine learning)","level":2,"score":0.3405361771583557},{"id":"https://openalex.org/C10229987","wikidata":"https://www.wikidata.org/wiki/Q17083028","display_name":"Incremental decision tree","level":4,"score":0.3394697904586792},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.18081018328666687},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.16791173815727234},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1301051676273346},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2837614.2837664","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2837614.2837664","pdf_url":"http://dl.acm.org/ft_gateway.cfm?id=2837664&type=pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.714.2178","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.714.2178","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.engr.illinois.edu/%7Egarg11/papers/dt-ice.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1145/2837614.2837664","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2837614.2837664","pdf_url":"http://dl.acm.org/ft_gateway.cfm?id=2837664&type=pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","raw_type":"proceedings-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7099999785423279}],"awards":[{"id":"https://openalex.org/G389929128","display_name":null,"funder_award_id":"FA8750-13-2-0008","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G4713059963","display_name":null,"funder_award_id":"FA8750","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G5643987864","display_name":null,"funder_award_id":"FA8750-13-2-0008","funder_id":"https://openalex.org/F4320337531","funder_display_name":"Defense Sciences Office, DARPA"},{"id":"https://openalex.org/G5921281487","display_name":null,"funder_award_id":"number","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6335147841","display_name":null,"funder_award_id":"1138994","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320337531","display_name":"Defense Sciences Office, DARPA","ror":"https://ror.org/0447fe631"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2185676247.pdf","grobid_xml":"https://content.openalex.org/works/W2185676247.grobid-xml"},"referenced_works_count":72,"referenced_works":["https://openalex.org/W1176919","https://openalex.org/W103680623","https://openalex.org/W145069693","https://openalex.org/W600081262","https://openalex.org/W1013235724","https://openalex.org/W1498946538","https://openalex.org/W1504694836","https://openalex.org/W1510368738","https://openalex.org/W1515020792","https://openalex.org/W1520252399","https://openalex.org/W1525169782","https://openalex.org/W1526922602","https://openalex.org/W1531054827","https://openalex.org/W1545681762","https://openalex.org/W1549166962","https://openalex.org/W1552077729","https://openalex.org/W1563374593","https://openalex.org/W1565898282","https://openalex.org/W1590437595","https://openalex.org/W1606177908","https://openalex.org/W1656403910","https://openalex.org/W1765120705","https://openalex.org/W1908450151","https://openalex.org/W1925669739","https://openalex.org/W1966242183","https://openalex.org/W1979603971","https://openalex.org/W1983119041","https://openalex.org/W1989445634","https://openalex.org/W1995875735","https://openalex.org/W1999625645","https://openalex.org/W2040870580","https://openalex.org/W2043100293","https://openalex.org/W2048679005","https://openalex.org/W2094878426","https://openalex.org/W2098022036","https://openalex.org/W2098039922","https://openalex.org/W2098095758","https://openalex.org/W2098278465","https://openalex.org/W2102928769","https://openalex.org/W2107794009","https://openalex.org/W2108776051","https://openalex.org/W2119467398","https://openalex.org/W2119821739","https://openalex.org/W2121717408","https://openalex.org/W2125055259","https://openalex.org/W2129113961","https://openalex.org/W2132661148","https://openalex.org/W2135322712","https://openalex.org/W2139709458","https://openalex.org/W2142481893","https://openalex.org/W2148177688","https://openalex.org/W2148193377","https://openalex.org/W2149706766","https://openalex.org/W2161253570","https://openalex.org/W2162284942","https://openalex.org/W2170322991","https://openalex.org/W2246217019","https://openalex.org/W2247845964","https://openalex.org/W2276356546","https://openalex.org/W2280703106","https://openalex.org/W2295903414","https://openalex.org/W2911867448","https://openalex.org/W2949530084","https://openalex.org/W4256477861","https://openalex.org/W4285719527","https://openalex.org/W4403705736","https://openalex.org/W6629794218","https://openalex.org/W6630511988","https://openalex.org/W6632737755","https://openalex.org/W6684718516","https://openalex.org/W6695642134","https://openalex.org/W6738852829"],"related_works":["https://openalex.org/W1982169401","https://openalex.org/W1648970942","https://openalex.org/W2030894524","https://openalex.org/W2356463514","https://openalex.org/W4387869645","https://openalex.org/W2120748120","https://openalex.org/W2591672004","https://openalex.org/W2143508752","https://openalex.org/W97367898","https://openalex.org/W4243803609"],"abstract_inverted_index":{"Inductive":[0],"invariants":[1],"can":[2],"be":[3],"robustly":[4],"synthesized":[5],"using":[6,74],"a":[7,14,80,120],"learning":[8,35,48,56,60,82],"model":[9,39,86],"where":[10],"the":[11,19,33,93,102,111],"teacher":[12],"is":[13,88,115],"program":[15,23],"verifier":[16],"who":[17],"instructs":[18],"learner":[20],"through":[21],"concrete":[22],"configurations,":[24],"classified":[25],"as":[26],"positive,":[27],"negative,":[28],"and":[29,104,108,117],"implications.":[30],"We":[31,77,100],"propose":[32],"first":[34],"algorithms":[36,57],"in":[37,58,84],"this":[38,85],"with":[40],"implication":[41,63],"counter-examples":[42],"that":[43,87,110],"are":[44],"based":[45],"on":[46],"machine":[47,59],"techniques.":[49],"In":[50],"particular,":[51],"we":[52],"extend":[53],"classical":[54],"decision-tree":[55,81],"to":[61,69,90,92],"handle":[62],"samples,":[64],"building":[65],"new":[66],"scalable":[67],"ways":[68],"construct":[70],"small":[71],"decision":[72],"trees":[73],"statistical":[75],"measures.":[76],"also":[78],"develop":[79],"algorithm":[83],"guaranteed":[89],"converge":[91],"right":[94],"concept":[95],"(invariant)":[96],"if":[97],"one":[98],"exists.":[99],"implement":[101],"learners":[103],"an":[105],"appropriate":[106],"teacher,":[107],"show":[109],"resulting":[112],"invariant":[113],"synthesis":[114],"efficient":[116],"convergent":[118],"for":[119],"large":[121],"suite":[122],"of":[123],"programs.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":25},{"year":2019,"cited_by_count":25},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":21},{"year":2016,"cited_by_count":16},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-11T08:14:18.477133","created_date":"2025-10-10T00:00:00"}