{"id":"https://openalex.org/W3172723392","doi":"https://doi.org/10.46298/lmcs-18(1:35)2022","title":"Hilbert's Tenth Problem in Coq (Extended Version)","display_name":"Hilbert's Tenth Problem in Coq (Extended Version)","publication_year":2022,"publication_date":"2022-03-01","ids":{"openalex":"https://openalex.org/W3172723392","doi":"https://doi.org/10.46298/lmcs-18(1:35)2022","mag":"3172723392"},"language":"en","primary_location":{"id":"doi:10.46298/lmcs-18(1:35)2022","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-18(1:35)2022","pdf_url":"https://lmcs.episciences.org/9153/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/9153/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069943669","display_name":"Dominique Larchey-Wendling","orcid":"https://orcid.org/0000-0001-9860-7203"},"institutions":[{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Dominique Larchey-Wendling","raw_affiliation_strings":["Laboratoire Lorrain de Recherche en Informatique et ses Applications"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","institution_ids":["https://openalex.org/I4210121838"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080496189","display_name":"Yannick Forster","orcid":"https://orcid.org/0000-0002-8676-9819"},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Yannick Forster","raw_affiliation_strings":["Saarland Univ., Saarbrucken"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saarland Univ., Saarbrucken","institution_ids":["https://openalex.org/I91712215"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1521,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.45109846,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"Volume 18, Issue 1","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9995999932289124,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9995999932289124,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9977999925613403,"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/T11567","display_name":"semigroups and automata theory","score":0.9829999804496765,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/diophantine-equation","display_name":"Diophantine equation","score":0.9021475315093994},{"id":"https://openalex.org/keywords/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.714508056640625},{"id":"https://openalex.org/keywords/computability","display_name":"Computability","score":0.6791387796401978},{"id":"https://openalex.org/keywords/recursively-enumerable-set","display_name":"Recursively enumerable set","score":0.5509712100028992},{"id":"https://openalex.org/keywords/diophantine-set","display_name":"Diophantine set","score":0.5383845567703247},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5303075313568115},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5128057599067688},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.49957919120788574},{"id":"https://openalex.org/keywords/compiler","display_name":"Compiler","score":0.45539137721061707},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44015738368034363},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.43803712725639343},{"id":"https://openalex.org/keywords/proof-assistant","display_name":"Proof assistant","score":0.4343324303627014},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3602312207221985},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34769630432128906},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33678334951400757},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31637999415397644},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.21441161632537842},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.11690670251846313}],"concepts":[{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.9021475315093994},{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.714508056640625},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.6791387796401978},{"id":"https://openalex.org/C52703633","wikidata":"https://www.wikidata.org/wiki/Q676835","display_name":"Recursively enumerable set","level":3,"score":0.5509712100028992},{"id":"https://openalex.org/C40621787","wikidata":"https://www.wikidata.org/wiki/Q16251580","display_name":"Diophantine set","level":3,"score":0.5383845567703247},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5303075313568115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5128057599067688},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.49957919120788574},{"id":"https://openalex.org/C169590947","wikidata":"https://www.wikidata.org/wiki/Q47506","display_name":"Compiler","level":2,"score":0.45539137721061707},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44015738368034363},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.43803712725639343},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.4343324303627014},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3602312207221985},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34769630432128906},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33678334951400757},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31637999415397644},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.21441161632537842},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.11690670251846313},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.46298/lmcs-18(1:35)2022","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-18(1:35)2022","pdf_url":"https://lmcs.episciences.org/9153/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2003.04604","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.04604","pdf_url":"https://arxiv.org/pdf/2003.04604","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3172723392","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2003.04604.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-03359505v1","is_oa":true,"landing_page_url":"https://hal.inria.fr/hal-03359505","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.inria.fr/hal-03359505","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:doaj.org/article:e84583266fa84958b0815be41ed22b5b","is_oa":true,"landing_page_url":"https://doaj.org/article/e84583266fa84958b0815be41ed22b5b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 18, Issue 1 (2022)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2003.04604","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2003.04604","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.46298/lmcs-18(1:35)2022","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-18(1:35)2022","pdf_url":"https://lmcs.episciences.org/9153/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3172723392.pdf","grobid_xml":"https://content.openalex.org/works/W3172723392.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W50191166","https://openalex.org/W62585087","https://openalex.org/W1964691638","https://openalex.org/W1983561917","https://openalex.org/W1997517079","https://openalex.org/W2004193076","https://openalex.org/W2012140001","https://openalex.org/W2045033949","https://openalex.org/W2059054133","https://openalex.org/W2082956932","https://openalex.org/W2096478770","https://openalex.org/W2114804254","https://openalex.org/W2137317612","https://openalex.org/W2328598177","https://openalex.org/W2584219801","https://openalex.org/W2585437719","https://openalex.org/W2746877179","https://openalex.org/W2769209754","https://openalex.org/W2772834916","https://openalex.org/W2794525229","https://openalex.org/W2804959061","https://openalex.org/W2887880196","https://openalex.org/W2895878038","https://openalex.org/W2895928777","https://openalex.org/W2906883693","https://openalex.org/W2907653511","https://openalex.org/W2941295182","https://openalex.org/W2953833525","https://openalex.org/W2953924437","https://openalex.org/W2965156518","https://openalex.org/W2978345188","https://openalex.org/W2978388349","https://openalex.org/W2978733758","https://openalex.org/W2991106333","https://openalex.org/W3003294284","https://openalex.org/W3130727218","https://openalex.org/W3172723392","https://openalex.org/W3173441168","https://openalex.org/W4237970627","https://openalex.org/W6891796055","https://openalex.org/W6893791045","https://openalex.org/W6929297288","https://openalex.org/W6929904570","https://openalex.org/W6966372878"],"related_works":["https://openalex.org/W2978388349","https://openalex.org/W1968562989","https://openalex.org/W2162634125","https://openalex.org/W2333608964","https://openalex.org/W1965442792","https://openalex.org/W2277411487","https://openalex.org/W1594204914","https://openalex.org/W2967076817","https://openalex.org/W2898484043","https://openalex.org/W2069207426","https://openalex.org/W1480087061","https://openalex.org/W2476084925","https://openalex.org/W1600661924","https://openalex.org/W3004024630","https://openalex.org/W117725373","https://openalex.org/W2132317835","https://openalex.org/W2971913802","https://openalex.org/W2772712032","https://openalex.org/W3186888504","https://openalex.org/W2112754349"],"abstract_inverted_index":{"We":[0,50],"formalise":[1],"the":[2,25,30,76],"undecidability":[3],"of":[4,6,29],"solvability":[5],"Diophantine":[7,83],"equations,":[8],"i.e.":[9],"polynomial":[10],"equations":[11],"over":[12],"natural":[13],"numbers,":[14],"in":[15,40],"Coq's":[16],"constructive":[17],"type":[18],"theory.":[19],"To":[20],"do":[21],"so,":[22],"we":[23,74],"give":[24,91],"first":[26],"full":[27],"mechanisation":[28],"Davis-Putnam-Robinson-Matiyasevich":[31],"theorem,":[32],"stating":[33],"that":[34,81],"every":[35,82],"recursively":[36],"enumerable":[37],"problem":[38],"--":[39,47],"our":[41],"case":[42],"by":[43,57,65,87],"a":[44,59,92],"Minsky":[45,99],"machine":[46],"is":[48,85],"Diophantine.":[49],"obtain":[51],"an":[52],"elegant":[53],"and":[54,64,79,90],"comprehensible":[55],"proof":[56],"using":[58],"synthetic":[60],"approach":[61],"to":[62,98],"computability":[63],"introducing":[66],"Conway's":[67],"FRACTRAN":[68],"language":[69],"as":[70],"intermediate":[71],"layer.":[72],"Additionally,":[73],"prove":[75],"reverse":[77],"direction":[78],"show":[80],"relation":[84],"recognisable":[86],"$\\mu$-recursive":[88,96],"functions":[89,97],"certified":[93],"compiler":[94],"from":[95],"machines.":[100]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}