{"id":"https://openalex.org/W2963999609","doi":"https://doi.org/10.1109/cec.2016.7744352","title":"Automatically proving mathematical theorems with evolutionary algorithms and proof assistants","display_name":"Automatically proving mathematical theorems with evolutionary algorithms and proof assistants","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2963999609","doi":"https://doi.org/10.1109/cec.2016.7744352","mag":"2963999609"},"language":"en","primary_location":{"id":"doi:10.1109/cec.2016.7744352","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2016.7744352","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Congress on Evolutionary Computation (CEC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042474229","display_name":"Li-An Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Li-An Yang","raw_affiliation_strings":["Department of Computer Science, National Chiao Tung University, HsinChu City, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, National Chiao Tung University, HsinChu City, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072397410","display_name":"Jui-Pin Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Jui-Pin Liu","raw_affiliation_strings":["Department of Computer Science, National Chiao Tung University, HsinChu City, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, National Chiao Tung University, HsinChu City, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023236233","display_name":"Chao-Hong Chen","orcid":"https://orcid.org/0000-0002-9314-8105"},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chao-Hong Chen","raw_affiliation_strings":["Department of Computer Science, National Chiao Tung University, HsinChu City, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, National Chiao Tung University, HsinChu City, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076296753","display_name":"Ying-ping Chen","orcid":"https://orcid.org/0000-0002-5979-6926"},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Ying-ping Chen","raw_affiliation_strings":["Department of Computer Science, National Chiao Tung University, HsinChu City, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, National Chiao Tung University, HsinChu City, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I148366613"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"4421","last_page":"4428"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9998000264167786,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9998000264167786,"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/T11574","display_name":"Artificial Intelligence in Games","score":0.9945999979972839,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9929999709129333,"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/mathematical-proof","display_name":"Mathematical proof","score":0.8885065317153931},{"id":"https://openalex.org/keywords/proof-assistant","display_name":"Proof assistant","score":0.738099992275238},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7227617502212524},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.720501184463501},{"id":"https://openalex.org/keywords/formal-proof","display_name":"Formal proof","score":0.670219898223877},{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"Computer-assisted proof","score":0.6250371932983398},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.5139779448509216},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.492933988571167},{"id":"https://openalex.org/keywords/analytic-proof","display_name":"Analytic proof","score":0.4786290228366852},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.45299598574638367},{"id":"https://openalex.org/keywords/structural-proof-theory","display_name":"Structural proof theory","score":0.4509170353412628},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.4438468813896179},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4410230815410614},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22762387990951538}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8885065317153931},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.738099992275238},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7227617502212524},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.720501184463501},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.670219898223877},{"id":"https://openalex.org/C173613240","wikidata":"https://www.wikidata.org/wiki/Q1150675","display_name":"Computer-assisted proof","level":3,"score":0.6250371932983398},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.5139779448509216},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.492933988571167},{"id":"https://openalex.org/C135754263","wikidata":"https://www.wikidata.org/wiki/Q4751136","display_name":"Analytic proof","level":3,"score":0.4786290228366852},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.45299598574638367},{"id":"https://openalex.org/C195653647","wikidata":"https://www.wikidata.org/wiki/Q7625047","display_name":"Structural proof theory","level":4,"score":0.4509170353412628},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.4438468813896179},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4410230815410614},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22762387990951538},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cec.2016.7744352","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2016.7744352","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Congress on Evolutionary Computation (CEC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.5799999833106995}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322795","display_name":"Ministry of Science and Technology, Taiwan","ror":"https://ror.org/02kv4zf79"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1483736078","https://openalex.org/W1513108299","https://openalex.org/W1559956479","https://openalex.org/W1576818901","https://openalex.org/W1775913388","https://openalex.org/W1973312452","https://openalex.org/W2069403261","https://openalex.org/W2089241138","https://openalex.org/W2092699841","https://openalex.org/W2100604298","https://openalex.org/W2112161977","https://openalex.org/W2112774031","https://openalex.org/W2114012357","https://openalex.org/W2126316555","https://openalex.org/W2127338150","https://openalex.org/W2132453167","https://openalex.org/W2186501980","https://openalex.org/W2203107069","https://openalex.org/W2257979135","https://openalex.org/W2294628582","https://openalex.org/W2505947701","https://openalex.org/W2798401172","https://openalex.org/W4213333889","https://openalex.org/W4237236902","https://openalex.org/W4301666354","https://openalex.org/W4403406779","https://openalex.org/W6630315736","https://openalex.org/W6630778951","https://openalex.org/W6981846578"],"related_works":["https://openalex.org/W1496026483","https://openalex.org/W2162495973","https://openalex.org/W2119682046","https://openalex.org/W4234403895","https://openalex.org/W3163122332","https://openalex.org/W1541513585","https://openalex.org/W187835144","https://openalex.org/W2491370528","https://openalex.org/W1610564136","https://openalex.org/W2040769847"],"abstract_inverted_index":{"Mathematical":[0],"theorems":[1,17,185,194,206],"are":[2,230,242],"human":[3,39],"knowledge":[4],"able":[5],"to":[6,74,78,83,89,105,114,153,158,181],"be":[7,55,106,208],"accumulated":[8],"in":[9,47,97,123,151,175,216],"the":[10,25,29,48,71,75,79,98,131,135,141,148,164,171,189,212,218,233,238],"form":[11],"of":[12,36,100,118,133,167,198,204,227],"symbolic":[13],"representation,":[14],"and":[15,28,57,64,108,120,144,202,224,232],"proving":[16],"has":[18],"been":[19,45,111],"considered":[20,56],"intelligent":[21],"behavior.":[22],"Based":[23],"on":[24],"BHK":[26],"interpretation":[27],"Curry-Howard":[30],"isomorphism,":[31],"proof":[32,61,67,145,149,220],"assistants,":[33,146],"software":[34],"capable":[35],"interacting":[37],"with":[38,237],"for":[40,93,126],"constructing":[41],"formal":[42,94,156],"proofs,":[43],"have":[44,110],"developed":[46,234],"past":[49],"several":[50,128],"decades.":[51,129],"Since":[52],"proofs":[53,95,157],"can":[54],"expressed":[58],"as":[59,140,147,186,188,244],"programs,":[60],"assistants":[62],"simplify":[63],"verify":[65],"a":[66,116,159],"by":[68,210],"computationally":[69],"evaluating":[70],"program":[72,142],"corresponding":[73],"proof.":[76],"Thanks":[77],"transformation":[80],"from":[81,195],"logic":[82,161],"computation,":[84],"it":[85],"is":[86,163],"now":[87],"possible":[88],"generate":[90],"or":[91],"search":[92],"directly":[96],"realm":[99],"computation.":[101],"Evolutionary":[102],"algorithms,":[103,139],"known":[104],"flexible":[107],"versatile,":[109],"successfully":[112],"applied":[113],"handle":[115],"variety":[117],"scientific":[119],"engineering":[121],"problems":[122],"numerous":[124],"disciplines":[125],"also":[127],"Examining":[130],"feasibility":[132],"establishing":[134],"link":[136],"between":[137],"evolutionary":[138],"generator,":[143],"verifier,":[150],"order":[152],"automatically":[154,183],"find":[155],"given":[160],"sentence":[162],"primary":[165],"goal":[166],"this":[168,228],"study.":[169],"In":[170],"article,":[172],"we":[173],"describe":[174],"detail":[176],"our":[177],"first,":[178],"ad-hoc":[179],"attempt":[180],"fully":[182],"prove":[184],"well":[187],"preliminary":[190],"results.":[191],"Ten":[192],"simple":[193],"various":[196],"branches":[197],"mathematics":[199],"were":[200],"proven,":[201],"most":[203],"these":[205],"cannot":[207],"proven":[209],"using":[211],"tactic":[213],"auto":[214],"alone":[215],"Coq,":[217],"adopted":[219],"assistant.":[221],"The":[222],"implication":[223],"potential":[225],"influence":[226],"study":[229],"discussed,":[231],"source":[235],"code":[236],"obtained":[239],"experimental":[240],"results":[241],"released":[243],"open":[245],"source.":[246]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}