{"id":"https://openalex.org/W2056827464","doi":"https://doi.org/10.2307/2586729","title":"Witnessing functions in bounded arithmetic and search problems","display_name":"Witnessing functions in bounded arithmetic and search problems","publication_year":1998,"publication_date":"1998-09-01","ids":{"openalex":"https://openalex.org/W2056827464","doi":"https://doi.org/10.2307/2586729","mag":"2056827464"},"language":"en","primary_location":{"id":"doi:10.2307/2586729","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586729","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","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/A5091149786","display_name":"Mario Chiari","orcid":null},"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"]},{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}],"countries":["CZ","SK"],"is_corresponding":false,"raw_author_name":"Mario Chiari","raw_affiliation_strings":["Mathematical Institute, Academy of Sciences, \u017ditn\u00e1 25, Prague, 115 67, Czech Republic E-mail:","Mathematical Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, Academy of Sciences, \u017ditn\u00e1 25, Prague, 115 67, Czech Republic E-mail:","institution_ids":["https://openalex.org/I4210120266"]},{"raw_affiliation_string":"Mathematical Institute","institution_ids":["https://openalex.org/I4210120676"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069803587","display_name":"Jan Kraj\u0131\u0301\u010dek","orcid":"https://orcid.org/0000-0003-0670-3957"},"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"]},{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]},{"id":"https://openalex.org/I4210155092","display_name":"Czech Academy of Sciences, Institute of Computer Science","ror":"https://ror.org/0496n6574","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210155092"]}],"countries":["CZ","SK"],"is_corresponding":false,"raw_author_name":"Jan Kraj\u00ed\u010dek","raw_affiliation_strings":["Mathematical Institute and Institute of Computer Science, Academy of Sciences, \u017ditn\u00e1 25, Prague, 115 67, Czech Republic E-mail:","Mathematical Institute and Institute of Computer Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute and Institute of Computer Science, Academy of Sciences, \u017ditn\u00e1 25, Prague, 115 67, Czech Republic E-mail:","institution_ids":["https://openalex.org/I4210120266"]},{"raw_affiliation_string":"Mathematical Institute and Institute of Computer Science","institution_ids":["https://openalex.org/I4210120676","https://openalex.org/I4210155092"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4611,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.82156688,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"63","issue":"3","first_page":"1095","last_page":"1115"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","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/T10720","display_name":"Complexity and Algorithms in Graphs","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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.996399998664856,"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":0.9929999709129333,"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/pigeonhole-principle","display_name":"Pigeonhole principle","score":0.7667067050933838},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.7360326051712036},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6910102367401123},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6472997665405273},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.6090623736381531},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.530082106590271},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5194551348686218},{"id":"https://openalex.org/keywords/conservative-extension","display_name":"Conservative extension","score":0.4846423268318176},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.44149404764175415},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44035691022872925},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4375235438346863},{"id":"https://openalex.org/keywords/second-order-arithmetic","display_name":"Second-order arithmetic","score":0.43644213676452637},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.42714375257492065},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38526037335395813},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3500346541404724},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29838913679122925},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08661094307899475}],"concepts":[{"id":"https://openalex.org/C171988527","wikidata":"https://www.wikidata.org/wiki/Q188276","display_name":"Pigeonhole principle","level":2,"score":0.7667067050933838},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7360326051712036},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6910102367401123},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6472997665405273},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.6090623736381531},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.530082106590271},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5194551348686218},{"id":"https://openalex.org/C2780432614","wikidata":"https://www.wikidata.org/wiki/Q864213","display_name":"Conservative extension","level":2,"score":0.4846423268318176},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.44149404764175415},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44035691022872925},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4375235438346863},{"id":"https://openalex.org/C65148605","wikidata":"https://www.wikidata.org/wiki/Q7442973","display_name":"Second-order arithmetic","level":3,"score":0.43644213676452637},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.42714375257492065},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38526037335395813},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3500346541404724},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29838913679122925},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08661094307899475},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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},{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2307/2586729","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586729","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183745583","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745583","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.49.4380","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.4380","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.ox.ac.uk/~krajicek/search.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6700000166893005,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W56285243","https://openalex.org/W560364776","https://openalex.org/W639289183","https://openalex.org/W1531368347","https://openalex.org/W1572440476","https://openalex.org/W1585510143","https://openalex.org/W1597020313","https://openalex.org/W1607926272","https://openalex.org/W1983604941","https://openalex.org/W1988083342","https://openalex.org/W2011612028","https://openalex.org/W2029390834","https://openalex.org/W2035004935","https://openalex.org/W2036656440","https://openalex.org/W2040404640","https://openalex.org/W2060270693","https://openalex.org/W2071204190","https://openalex.org/W2133313069","https://openalex.org/W2161149481","https://openalex.org/W2169713712","https://openalex.org/W2170605748","https://openalex.org/W2479478569","https://openalex.org/W2495451020","https://openalex.org/W2562830775","https://openalex.org/W2798789889","https://openalex.org/W4206266376","https://openalex.org/W4245266864","https://openalex.org/W4248733413","https://openalex.org/W4255046774","https://openalex.org/W4388289526"],"related_works":["https://openalex.org/W180613403","https://openalex.org/W1986380412","https://openalex.org/W2009666428","https://openalex.org/W2130229234","https://openalex.org/W2138856440","https://openalex.org/W1504491664","https://openalex.org/W36100467","https://openalex.org/W3207331746","https://openalex.org/W4321514130","https://openalex.org/W2056827464"],"abstract_inverted_index":{"Abstract":[0],"We":[1,37],"investigate":[2],"the":[3,39,55,69,77,83,89,95,106,110,135,140],"possibility":[4],"to":[5],"characterize":[6],"(multi)functions":[7,49,63],"that":[8,50,64,88,122,149],"are":[9,51,65],"-definable":[10,53,67],"with":[11,134],"small":[12],"i":[13,15],"(":[14],"=":[16],"1,":[17],"2,":[18],"3)":[19],"in":[20,27,54,68],"fragments":[21],"of":[22,29,45,48,62,102],"bounded":[23],"arithmetic":[24],"T":[25],"2":[26,116,131],"terms":[28],"natural":[30],"search":[31],"problems":[32],"defined":[33,153],"over":[34,82,94],"polynomial-time":[35],"structures.":[36],"obtain":[38],"following":[40],"results:":[41],"(1)":[42],"A":[43,73],"reformulation":[44],"known":[46],"characterizations":[47,61],"and":[52,57,66,132],"theories":[56],".":[58,71,85],"(2)":[59],"New":[60],"theory":[70,78,84,90,96],"(3)":[72],"new":[74],"non-conservation":[75],"result:":[76],"is":[79,91,126],"not":[80,92],"-conservative":[81,93],"To":[86],"prove":[87],",":[97,117,138],"we":[98],"present":[99],"two":[100,107],"examples":[101],"a":[103,115,127,130,133,155],"-principle":[104],"separating":[105],"theories:":[108],"(a)":[109],"weak":[111],"pigeonhole":[112],"principle":[113,142],"WPHP(":[114],"f,":[118],"g":[119,137],")":[120,147,162],"formalizing":[121,148],"no":[123,150],"function":[124,151],"f":[125,146,152],"bijection":[128],"between":[129],"inverse":[136],"(b)":[139],"iteration":[141],"Iter(":[143],"a,":[144],"R,":[145],"on":[154],"strict":[156],"partial":[157],"order":[158],"({0,\u2026,":[159],"a},":[160],"R":[161],"can":[163],"have":[164],"increasing":[165],"iterates.":[166]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":29},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}