{"id":"https://openalex.org/W2061456270","doi":"https://doi.org/10.1016/0168-0072(87)90017-0","title":"Nonconvergence, undecidability, and intractability in asymptotic problems","display_name":"Nonconvergence, undecidability, and intractability in asymptotic problems","publication_year":1987,"publication_date":"1987-01-01","ids":{"openalex":"https://openalex.org/W2061456270","doi":"https://doi.org/10.1016/0168-0072(87)90017-0","mag":"2061456270"},"language":"en","primary_location":{"id":"doi:10.1016/0168-0072(87)90017-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0168-0072(87)90017-0","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/2027.42/154144","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015848236","display_name":"Kevin J. Compton","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kevin J. Compton","raw_affiliation_strings":["EECS Department, University of Michigan, Ann Arbor, MI 48109, USA","EECS. Dept. University of Michigan Ann Arbor, MI 48109, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"EECS Department, University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"EECS. Dept. University of Michigan Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090166557","display_name":"C. Ward Henson","orcid":"https://orcid.org/0000-0003-1499-4432"},"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":"C. Ward Henson","raw_affiliation_strings":["Mathematics Department, University of Illinois, Urbana, IL 61801, USA","Mathematics Department , University of Illinois , Urbana, IL, 61801, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of Illinois, Urbana, IL 61801, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Mathematics Department , University of Illinois , Urbana, IL, 61801, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024923217","display_name":"Saharon Shelah","orcid":"https://orcid.org/0000-0003-0462-3152"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Saharon Shelah","raw_affiliation_strings":["EECS Department and Mathematics Department, University of Michigan, Ann Arbor, MI 48109, USA (Current address: Mathematics Dept., Hebrew Univ., Jerusalem, Israel)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"EECS Department and Mathematics Department, University of Michigan, Ann Arbor, MI 48109, USA (Current address: Mathematics Dept., Hebrew Univ., Jerusalem, Israel)","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015848236"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":null,"fwci":2.6706,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.89733903,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"36","issue":null,"first_page":"207","last_page":"224"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9965000152587891,"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/T11567","display_name":"semigroups and automata theory","score":0.9965000152587891,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9865000247955322,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9843000173568726,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/unary-operation","display_name":"Unary operation","score":0.8834883570671082},{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.8539239168167114},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8429626226425171},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6723501682281494},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5767184495925903},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5534878373146057},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5446147918701172},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.507602334022522},{"id":"https://openalex.org/keywords/asymptotic-analysis","display_name":"Asymptotic analysis","score":0.4927528202533722},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.4628294110298157},{"id":"https://openalex.org/keywords/asymptotic-formula","display_name":"Asymptotic formula","score":0.4535650908946991},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.4230741262435913},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4211660623550415},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4170273244380951},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2666533589363098},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0656648576259613},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.06221193075180054}],"concepts":[{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.8834883570671082},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.8539239168167114},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8429626226425171},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6723501682281494},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5767184495925903},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5534878373146057},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5446147918701172},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.507602334022522},{"id":"https://openalex.org/C119047807","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.4927528202533722},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.4628294110298157},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.4535650908946991},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.4230741262435913},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4211660623550415},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4170273244380951},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2666533589363098},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0656648576259613},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.06221193075180054},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/0168-0072(87)90017-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0168-0072(87)90017-0","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"},{"id":"pmh:oai:deepblue.lib.umich.edu:2027.42/154144","is_oa":true,"landing_page_url":"https://hdl.handle.net/2027.42/154144","pdf_url":"https://hdl.handle.net/2027.42/154144","source":{"id":"https://openalex.org/S4306400393","display_name":"Deep Blue (University of Michigan)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I27837315","host_organization_name":"University of Michigan","host_organization_lineage":["https://openalex.org/I27837315"],"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":"Technical Report"},{"id":"pmh:oai:deepblue.lib.umich.edu:2027.42/26912","is_oa":true,"landing_page_url":"http://hdl.handle.net/2027.42/26912>","pdf_url":"https://hdl.handle.net/2027.42/26912","source":{"id":"https://openalex.org/S4306400393","display_name":"Deep Blue (University of Michigan)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I27837315","host_organization_name":"University of Michigan","host_organization_lineage":["https://openalex.org/I27837315"],"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":"Article"}],"best_oa_location":{"id":"pmh:oai:deepblue.lib.umich.edu:2027.42/154144","is_oa":true,"landing_page_url":"https://hdl.handle.net/2027.42/154144","pdf_url":"https://hdl.handle.net/2027.42/154144","source":{"id":"https://openalex.org/S4306400393","display_name":"Deep Blue (University of Michigan)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I27837315","host_organization_name":"University of Michigan","host_organization_lineage":["https://openalex.org/I27837315"],"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":"Technical Report"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2061456270.pdf","grobid_xml":"https://content.openalex.org/works/W2061456270.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1513644114","https://openalex.org/W1519522813","https://openalex.org/W1968112027","https://openalex.org/W1985072883","https://openalex.org/W1990958546","https://openalex.org/W1992041151","https://openalex.org/W1996847651","https://openalex.org/W2008527519","https://openalex.org/W2013122733","https://openalex.org/W2020403120","https://openalex.org/W2022043776","https://openalex.org/W2034198367","https://openalex.org/W2048652909","https://openalex.org/W2085536555","https://openalex.org/W2090008352","https://openalex.org/W2335566765","https://openalex.org/W4206797071","https://openalex.org/W4235934183","https://openalex.org/W4244028915","https://openalex.org/W4246697543","https://openalex.org/W4254608674","https://openalex.org/W6630692274","https://openalex.org/W6630927324","https://openalex.org/W6655561421","https://openalex.org/W6659211631","https://openalex.org/W6662516986"],"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/W2020140696"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-17T08:19:37.847499","created_date":"2025-10-10T00:00:00"}