{"id":"https://openalex.org/W1989692246","doi":"https://doi.org/10.1145/1805950.1805952","title":"A tight Karp-Lipton collapse result in bounded arithmetic","display_name":"A tight Karp-Lipton collapse result in bounded arithmetic","publication_year":2010,"publication_date":"2010-07-01","ids":{"openalex":"https://openalex.org/W1989692246","doi":"https://doi.org/10.1145/1805950.1805952","mag":"1989692246"},"language":"en","primary_location":{"id":"doi:10.1145/1805950.1805952","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1805950.1805952","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational 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/A5042128349","display_name":"Olaf Beyersdorff","orcid":"https://orcid.org/0000-0002-2870-1648"},"institutions":[{"id":"https://openalex.org/I114112103","display_name":"Leibniz University Hannover","ror":"https://ror.org/0304hq317","country_code":"DE","type":"education","lineage":["https://openalex.org/I114112103"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Olaf Beyersdorff","raw_affiliation_strings":["Institut f\u00fcr Theoretische Informatik, Leibniz-Universit\u00e4t Hannover, Hannover, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Informatik, Leibniz-Universit\u00e4t Hannover, Hannover, Germany","institution_ids":["https://openalex.org/I114112103"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101792125","display_name":"Sebastian M\u00fcller","orcid":null},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sebastian M\u00fcller","raw_affiliation_strings":["Institut f\u00fcr Informatik, Humboldt-Universit\u00e4t zu Berlin, Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, Humboldt-Universit\u00e4t zu Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042128349"],"corresponding_institution_ids":["https://openalex.org/I114112103"],"apc_list":null,"apc_paid":null,"fwci":2.08243861,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.85612657,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"11","issue":"4","first_page":"1","last_page":"23"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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/T10720","display_name":"Complexity and Algorithms in Graphs","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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9990000128746033,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9962999820709229,"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/converse","display_name":"Converse","score":0.7749258875846863},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.743273913860321},{"id":"https://openalex.org/keywords/polynomial-hierarchy","display_name":"Polynomial hierarchy","score":0.7189478874206543},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6821363568305969},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.6192241907119751},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5026681423187256},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.4326311945915222},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.30009758472442627}],"concepts":[{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.7749258875846863},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.743273913860321},{"id":"https://openalex.org/C2776013622","wikidata":"https://www.wikidata.org/wiki/Q2103021","display_name":"Polynomial hierarchy","level":3,"score":0.7189478874206543},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6821363568305969},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6192241907119751},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5026681423187256},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.4326311945915222},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.30009758472442627},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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:10.1145/1805950.1805952","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1805950.1805952","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4228545556","display_name":null,"funder_award_id":"KO 1053/5-1KO 1053/5-2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W572171498","https://openalex.org/W1537230380","https://openalex.org/W1567771348","https://openalex.org/W1607926272","https://openalex.org/W1953985671","https://openalex.org/W1970089350","https://openalex.org/W1975790950","https://openalex.org/W1987520994","https://openalex.org/W1988083342","https://openalex.org/W1989978772","https://openalex.org/W1996192734","https://openalex.org/W2050186596","https://openalex.org/W2053094807","https://openalex.org/W2063158069","https://openalex.org/W2071204190","https://openalex.org/W2087012565","https://openalex.org/W2091961944","https://openalex.org/W2114598059","https://openalex.org/W2128026324","https://openalex.org/W2169748287","https://openalex.org/W2171353564","https://openalex.org/W2331432079","https://openalex.org/W4243643814"],"related_works":["https://openalex.org/W4224299360","https://openalex.org/W4388962799","https://openalex.org/W2041517264","https://openalex.org/W1522180487","https://openalex.org/W4294789866","https://openalex.org/W1969386550","https://openalex.org/W2982557863","https://openalex.org/W2590361123","https://openalex.org/W1575303034","https://openalex.org/W2057722348"],"abstract_inverted_index":{"Cook":[0,53,86],"and":[1,32,54,87],"Kraj\u00ed\u010dek":[2],"have":[3],"recently":[4],"obtained":[5],"the":[6,15,24,29,43,76],"following":[7],"Karp-Lipton":[8],"collapse":[9,34],"result":[10,59],"in":[11,37,62],"bounded":[12],"arithmetic:":[13],"if":[14],"theory":[16],"PV":[17,38,63],"proves":[18],"NP\u2286":[19],"P/":[20],"poly":[21],",":[22],"then":[23],"polynomial":[25],"hierarchy":[26],"collapses":[27],"to":[28,110],"Boolean":[30],"hierarchy,":[31],"this":[33,58],"is":[35],"provable":[36],".":[39],"Here":[40],"we":[41,74,91],"show":[42,103],"converse":[44],"implication,":[45],"thus":[46],"answering":[47],"an":[48],"open":[49],"question":[50],"posed":[51],"by":[52,60,85],"Kraj\u00ed\u010dek.":[55,88],"We":[56,101],"obtain":[57,92],"formalizing":[61],"a":[64],"hard/easy":[65],"argument":[66],"of":[67,78,113],"Buhrman":[68],"et":[69],"al.":[70],"[2003].":[71],"In":[72,89],"addition,":[73],"continue":[75],"investigation":[77],"propositional":[79],"proof":[80,97],"systems":[81,98,107],"using":[82,99],"advice,":[83],"initiated":[84],"particular,":[90],"several":[93],"optimality":[94],"results":[95],"for":[96],"advice.":[100],"further":[102],"that":[104],"these":[105],"optimal":[106],"are":[108],"equivalent":[109],"natural":[111],"extensions":[112],"Frege":[114],"systems.":[115]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}