{"id":"https://openalex.org/W3209732136","doi":"https://doi.org/10.1145/3519935.3519958","title":"A strong version of Cobham\u2019s theorem","display_name":"A strong version of Cobham\u2019s theorem","publication_year":2022,"publication_date":"2022-06-09","ids":{"openalex":"https://openalex.org/W3209732136","doi":"https://doi.org/10.1145/3519935.3519958","mag":"3209732136"},"language":"en","primary_location":{"id":"doi:10.1145/3519935.3519958","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3519935.3519958","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"preprint","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/A5057206285","display_name":"Philipp Hieronymi","orcid":null},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Philipp Hieronymi","raw_affiliation_strings":["University of Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"University of Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059665527","display_name":"Christian Schulz","orcid":"https://orcid.org/0000-0002-2823-3506"},"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":"Christian Schulz","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":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057206285"],"corresponding_institution_ids":["https://openalex.org/I135140700"],"apc_list":null,"apc_paid":null,"fwci":0.79004329,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.62224396,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1172","last_page":"1179"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T11567","display_name":"semigroups and automata theory","score":0.9987999796867371,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.9474142789840698},{"id":"https://openalex.org/keywords/presburger-arithmetic","display_name":"Presburger arithmetic","score":0.8765286207199097},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.867951512336731},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6683095097541809},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.6258254051208496},{"id":"https://openalex.org/keywords/fragment","display_name":"Fragment (logic)","score":0.509077250957489},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48522189259529114},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4827424883842468},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.44978487491607666},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3727647364139557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2021094262599945},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1470312774181366}],"concepts":[{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.9474142789840698},{"id":"https://openalex.org/C5852641","wikidata":"https://www.wikidata.org/wiki/Q956059","display_name":"Presburger arithmetic","level":3,"score":0.8765286207199097},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.867951512336731},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6683095097541809},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.6258254051208496},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.509077250957489},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48522189259529114},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4827424883842468},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.44978487491607666},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3727647364139557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2021094262599945},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1470312774181366},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3519935.3519958","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3519935.3519958","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1520256591","https://openalex.org/W1575834508","https://openalex.org/W1964874178","https://openalex.org/W1994777467","https://openalex.org/W2003019252","https://openalex.org/W2009486845","https://openalex.org/W2030999998","https://openalex.org/W2052875987","https://openalex.org/W2058960916","https://openalex.org/W2085356622","https://openalex.org/W2131663704","https://openalex.org/W2163696969","https://openalex.org/W2169851573","https://openalex.org/W2310773057","https://openalex.org/W2407481752","https://openalex.org/W2801580804","https://openalex.org/W3106284779","https://openalex.org/W3127768611","https://openalex.org/W3183923497","https://openalex.org/W4205178514","https://openalex.org/W4238159413","https://openalex.org/W4241862332"],"related_works":["https://openalex.org/W2972379433","https://openalex.org/W1501430220","https://openalex.org/W2989332944","https://openalex.org/W2021891065","https://openalex.org/W2583549044","https://openalex.org/W2119045600","https://openalex.org/W2584984136","https://openalex.org/W2962928105","https://openalex.org/W2170336571","https://openalex.org/W3101316517"],"abstract_inverted_index":{"Let":[0],"k,\u2113\u2265":[1],"2":[2],"be":[3,41,46],"two":[4],"multiplicatively":[5],"independent":[6],"integers.":[7],"Cobham's":[8],"famous":[9],"theorem":[10,76],"states":[11],"that":[12,49,79],"a":[13,74],"set":[14],"X\u2286":[15,39],"\u2115":[16],"is":[17,27,67,70,86],"both":[18,50],"k-recognizable":[19],"and":[20,23,52],"\u2113-recognizable":[21,47],"if":[22,25],"only":[24],"it":[26],"definable":[28,56],"in":[29,57,71],"Presburger":[30,58],"arithmetic.":[31,59],"Here":[32],"we":[33],"show":[34],"the":[35,61,80],"following":[36],"strengthening:":[37],"let":[38,43],"\u2115m":[40],"k-recognizable,":[42],"Y\u2286":[44],"\u2115n":[45],"such":[48],"X":[51],"Y":[53],"are":[54],"not":[55],"Then":[60],"first-order":[62,81],"logical":[63,82],"theory":[64,83],"of":[65,77,84],"(\u2115,+,X,Y)":[66],"undecidable.":[68],"This":[69],"contrast":[72],"to":[73],"well-known":[75],"B\u00fcchi":[78],"(\u2115,+,X)":[85],"decidable.":[87]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
