{"id":"https://openalex.org/W2964003362","doi":"https://doi.org/10.1145/3087534","title":"Proof Complexity Modulo the Polynomial Hierarchy","display_name":"Proof Complexity Modulo the Polynomial Hierarchy","publication_year":2017,"publication_date":"2017-09-18","ids":{"openalex":"https://openalex.org/W2964003362","doi":"https://doi.org/10.1145/3087534","mag":"2964003362"},"language":"en","primary_location":{"id":"doi:10.1145/3087534","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3087534","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"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 Computation Theory","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/A5107271836","display_name":"Hubie Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I110594554","display_name":"Ikerbasque","ror":"https://ror.org/01cc3fy72","country_code":"ES","type":"other","lineage":["https://openalex.org/I110594554"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Hubie Chen","raw_affiliation_strings":["Universidad del Pa\u00ed Vasco and IKERBASQUE, Basque Foundation for Science, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad del Pa\u00ed Vasco and IKERBASQUE, Basque Foundation for Science, Spain","institution_ids":["https://openalex.org/I110594554"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5107271836"],"corresponding_institution_ids":["https://openalex.org/I110594554"],"apc_list":null,"apc_paid":null,"fwci":1.7007,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.86670257,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"9","issue":"3","first_page":"1","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9998999834060669,"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/T10142","display_name":"Formal Methods in Verification","score":0.9998999834060669,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9993000030517578,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9952999949455261,"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/proof-complexity","display_name":"Proof complexity","score":0.8028457164764404},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6502178907394409},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.6453078985214233},{"id":"https://openalex.org/keywords/structural-proof-theory","display_name":"Structural proof theory","score":0.62126225233078},{"id":"https://openalex.org/keywords/direct-proof","display_name":"Direct proof","score":0.6077823042869568},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.574128270149231},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.5724524855613708},{"id":"https://openalex.org/keywords/combinatorial-proof","display_name":"Combinatorial proof","score":0.5082520842552185},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.49271562695503235},{"id":"https://openalex.org/keywords/analytic-proof","display_name":"Analytic proof","score":0.4742359519004822},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4686654806137085},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4117431640625},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32007846236228943},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23843327164649963},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.23438304662704468}],"concepts":[{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.8028457164764404},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6502178907394409},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.6453078985214233},{"id":"https://openalex.org/C195653647","wikidata":"https://www.wikidata.org/wiki/Q7625047","display_name":"Structural proof theory","level":4,"score":0.62126225233078},{"id":"https://openalex.org/C161505775","wikidata":"https://www.wikidata.org/wiki/Q3240280","display_name":"Direct proof","level":2,"score":0.6077823042869568},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.574128270149231},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.5724524855613708},{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.5082520842552185},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.49271562695503235},{"id":"https://openalex.org/C135754263","wikidata":"https://www.wikidata.org/wiki/Q4751136","display_name":"Analytic proof","level":3,"score":0.4742359519004822},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4686654806137085},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4117431640625},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32007846236228943},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23843327164649963},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.23438304662704468},{"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/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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3087534","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3087534","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"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 Computation Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4885224720","display_name":null,"funder_award_id":"UFI 11/45","funder_id":"https://openalex.org/F4320321919","funder_display_name":"Euskal Herriko Unibertsitatea"}],"funders":[{"id":"https://openalex.org/F4320321919","display_name":"Euskal Herriko Unibertsitatea","ror":"https://ror.org/000xsnr85"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W5750292","https://openalex.org/W25993968","https://openalex.org/W45235819","https://openalex.org/W53088276","https://openalex.org/W54881092","https://openalex.org/W88271430","https://openalex.org/W119782953","https://openalex.org/W1480301700","https://openalex.org/W1482661140","https://openalex.org/W1525848078","https://openalex.org/W1567053297","https://openalex.org/W1817491722","https://openalex.org/W1851471023","https://openalex.org/W1852359712","https://openalex.org/W1976876676","https://openalex.org/W1979753555","https://openalex.org/W1996660205","https://openalex.org/W2014195574","https://openalex.org/W2047237020","https://openalex.org/W2069767473","https://openalex.org/W2084384424","https://openalex.org/W2092984557","https://openalex.org/W2098397367","https://openalex.org/W2171790376","https://openalex.org/W2339728308","https://openalex.org/W2407293324","https://openalex.org/W2407913417","https://openalex.org/W2612288690","https://openalex.org/W2757756903","https://openalex.org/W2887013560","https://openalex.org/W2985554528","https://openalex.org/W3103546459"],"related_works":["https://openalex.org/W2922318846","https://openalex.org/W3173957725","https://openalex.org/W3193550244","https://openalex.org/W2461509449","https://openalex.org/W3157478331","https://openalex.org/W3153156984","https://openalex.org/W2263677784","https://openalex.org/W2964003362","https://openalex.org/W3013034887","https://openalex.org/W1542569653"],"abstract_inverted_index":{"We":[0,57],"present":[1,10],"and":[2,86,92],"study":[3],"a":[4,40,59],"framework":[5,29],"in":[6,17,27,53,106],"which":[7,37],"one":[8],"can":[9,50],"alternation-based":[11],"lower":[12,95],"bounds":[13],"on":[14,69],"proof":[15,18,33,43,48,60,72,108],"length":[16],"systems":[19,44],"for":[20,46,97],"quantified":[21],"Boolean":[22],"formulas.":[23],"A":[24],"key":[25],"notion":[26],"this":[28],"is":[30,38,67],"that":[31,66],"of":[32,42,83,89,103],"system":[34,61,73],"ensemble":[35,62],",":[36],"(essentially)":[39],"sequence":[41],"where,":[45],"each,":[47],"checking":[49],"be":[51],"performed":[52],"the":[54,70,84],"polynomial":[55],"hierarchy.":[56],"introduce":[58],"called":[63],"relaxing":[64,90,98],"QU-res":[65,91],"based":[68],"established":[71],"QU-resolution":[74],".":[75],"Our":[76],"main":[77],"results":[78,105],"include":[79],"an":[80,93],"exponential":[81,94],"separation":[82],"treelike":[85],"general":[87],"versions":[88],"bound":[96],"QU-res;":[99],"these":[100],"are":[101],"analogs":[102],"classical":[104],"propositional":[107],"complexity.":[109]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}