{"id":"https://openalex.org/W2811224246","doi":"https://doi.org/10.3233/com-180096","title":"Feasible set functions have small circuits","display_name":"Feasible set functions have small circuits","publication_year":2018,"publication_date":"2018-07-03","ids":{"openalex":"https://openalex.org/W2811224246","doi":"https://doi.org/10.3233/com-180096","mag":"2811224246"},"language":"en","primary_location":{"id":"doi:10.3233/com-180096","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-180096","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},"type":"article","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/A5084524620","display_name":"Arnold Beckmann","orcid":"https://orcid.org/0000-0001-7958-5790"},"institutions":[{"id":"https://openalex.org/I39586589","display_name":"Swansea University","ror":"https://ror.org/053fq8t95","country_code":"GB","type":"education","lineage":["https://openalex.org/I39586589"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Arnold Beckmann","raw_affiliation_strings":["Department of Computer Science, Swansea University, UK. a.beckmann@swansea.ac.uk"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Swansea University, UK. a.beckmann@swansea.ac.uk","institution_ids":["https://openalex.org/I39586589"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067079243","display_name":"Sam Buss","orcid":"https://orcid.org/0000-0003-3837-334X"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sam Buss","raw_affiliation_strings":["Department of Mathematics, University of California, San Diego, USA. sbuss@ucsd.edu"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, San Diego, USA. sbuss@ucsd.edu","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009749667","display_name":"Sy\u2010David Friedman","orcid":"https://orcid.org/0000-0001-8460-4394"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Sy-David Friedman","raw_affiliation_strings":["Kurt G\u00f6del Research Center, University of Vienna, Austria. sdf@logic.univie.ac.at"],"affiliations":[{"raw_affiliation_string":"Kurt G\u00f6del Research Center, University of Vienna, Austria. sdf@logic.univie.ac.at","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011254078","display_name":"Moritz M\u00fcller","orcid":null},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Moritz M\u00fcller","raw_affiliation_strings":["Kurt G\u00f6del Research Center, University of Vienna, Austria. moritz.mueller@univie.ac.at"],"affiliations":[{"raw_affiliation_string":"Kurt G\u00f6del Research Center, University of Vienna, Austria. moritz.mueller@univie.ac.at","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007592654","display_name":"Neil Thapen","orcid":"https://orcid.org/0000-0001-9734-5029"},"institutions":[{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Neil Thapen","raw_affiliation_strings":["Institute of Mathematics, Czech Academy of Sciences, Czech Republic. thapen@math.cas.cz"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Czech Academy of Sciences, Czech Republic. thapen@math.cas.cz","institution_ids":["https://openalex.org/I4210120266"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5084524620"],"corresponding_institution_ids":["https://openalex.org/I39586589"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10849845,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":"1","first_page":"67","last_page":"98"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9970999956130981,"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"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9937999844551086,"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/recursion","display_name":"Recursion (computer science)","score":0.5763014554977417},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5761055946350098},{"id":"https://openalex.org/keywords/transitive-closure","display_name":"Transitive closure","score":0.5548266172409058},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5315536856651306},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5214561820030212},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5169562697410583},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4947344958782196},{"id":"https://openalex.org/keywords/computability-theory","display_name":"Computability theory","score":0.4851735234260559},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.4226100444793701},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.41442179679870605},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35178762674331665},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35154518485069275},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13332802057266235}],"concepts":[{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.5763014554977417},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5761055946350098},{"id":"https://openalex.org/C128896722","wikidata":"https://www.wikidata.org/wiki/Q1501387","display_name":"Transitive closure","level":2,"score":0.5548266172409058},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5315536856651306},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5214561820030212},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5169562697410583},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4947344958782196},{"id":"https://openalex.org/C111142201","wikidata":"https://www.wikidata.org/wiki/Q818930","display_name":"Computability theory","level":2,"score":0.4851735234260559},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.4226100444793701},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.41442179679870605},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35178762674331665},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35154518485069275},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13332802057266235},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","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},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3233/com-180096","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-180096","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},{"id":"pmh:oai:cronfa.swan.ac.uk:cronfa40896","is_oa":false,"landing_page_url":"https://cronfa.swan.ac.uk/Record/cronfa40896","pdf_url":null,"source":{"id":"https://openalex.org/S4306401612","display_name":"Cronfa (Swansea University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39586589","host_organization_name":"Swansea University","host_organization_lineage":["https://openalex.org/I39586589"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1538838225","https://openalex.org/W1571979909","https://openalex.org/W1823991804","https://openalex.org/W1981324778","https://openalex.org/W2119608156","https://openalex.org/W2122092051","https://openalex.org/W2139824158","https://openalex.org/W2165293955","https://openalex.org/W2167784134","https://openalex.org/W2252118216","https://openalex.org/W2560447809","https://openalex.org/W2571490773","https://openalex.org/W4296119740"],"related_works":["https://openalex.org/W1553139688","https://openalex.org/W2371151875","https://openalex.org/W2136009070","https://openalex.org/W2362009423","https://openalex.org/W2391133415","https://openalex.org/W2012063573","https://openalex.org/W1982015164","https://openalex.org/W203725150","https://openalex.org/W4230967508","https://openalex.org/W1499233953"],"abstract_inverted_index":{"The":[0,26,39,65],"Cobham":[1],"Recursive":[2],"Set":[3],"Functions":[4],"(CRSF)":[5],"provide":[6],"an":[7],"analogue":[8],"of":[9,24,36,60,70,74],"polynomial":[10],"time":[11],"computation":[12],"which":[13],"applies":[14],"to":[15,51],"arbitrary":[16],"sets.":[17],"We":[18],"give":[19],"three":[20],"new":[21],"equivalent":[22],"characterizations":[23],"CRSF.":[25],"first":[27],"is":[28,41,67],"algebraic,":[29],"using":[30],"subset-bounded":[31,82],"recursion":[32],"and":[33,81],"a":[34,58,71],"form":[35],"Mostowski":[37],"collapse.":[38],"second":[40],"our":[42],"main":[43],"resul":[44],"t:":[45],"the":[46,54,75],"CRSF":[47],"functions":[48,55,77],"are":[49],"shown":[50],"be":[52],"precisely":[53],"computed":[56],"by":[57,78],"class":[59],"uniform,":[61],"infinitary,":[62],"Boolean":[63],"circuits.":[64],"third":[66],"in":[68],"terms":[69],"simple":[72],"extension":[73],"rudimentary":[76],"transitive":[79],"closure":[80],"recursion.":[83]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}