{"id":"https://openalex.org/W1505776303","doi":"https://doi.org/10.1007/978-3-642-39206-1_37","title":"Towards an Understanding of Polynomial Calculus: New Separations and Lower Bounds","display_name":"Towards an Understanding of Polynomial Calculus: New Separations and Lower Bounds","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1505776303","doi":"https://doi.org/10.1007/978-3-642-39206-1_37","mag":"1505776303"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-39206-1_37","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-39206-1_37","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","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":null,"display_name":"Yuval Filmus","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Yuval Filmus","raw_affiliation_strings":["University of Toronto, Toronto, Ontario, M5S 2E4, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Toronto, Toronto, Ontario, M5S 2E4, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024267515","display_name":"Massimo Lauria","orcid":"https://orcid.org/0000-0003-4003-3168"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Massimo Lauria","raw_affiliation_strings":["KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090900538","display_name":"Mladen Mik\u0161a","orcid":"https://orcid.org/0000-0002-5422-4267"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Mladen Mik\u0161a","raw_affiliation_strings":["KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003633660","display_name":"Jakob Nordstr\u0094\u00f6m","orcid":"https://orcid.org/0000-0002-2700-4285"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Jakob Nordstr\u00f6m","raw_affiliation_strings":["KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014450397","display_name":"Marc Vinyals","orcid":"https://orcid.org/0000-0002-1487-445X"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Marc Vinyals","raw_affiliation_strings":["KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"437","last_page":"448"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9991999864578247,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9990000128746033,"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":0.7297810316085815},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6717971563339233},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.5831542015075684},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5224822163581848},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49616798758506775},{"id":"https://openalex.org/keywords/linear-space","display_name":"Linear space","score":0.46609795093536377},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4520471394062042},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45069605112075806},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.4228188097476959},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.41377323865890503},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4070424437522888},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39171722531318665}],"concepts":[{"id":"https://openalex.org/C171988527","wikidata":"https://www.wikidata.org/wiki/Q188276","display_name":"Pigeonhole principle","level":2,"score":0.7297810316085815},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6717971563339233},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.5831542015075684},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5224822163581848},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49616798758506775},{"id":"https://openalex.org/C176370821","wikidata":"https://www.wikidata.org/wiki/Q1826459","display_name":"Linear space","level":2,"score":0.46609795093536377},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4520471394062042},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45069605112075806},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.4228188097476959},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.41377323865890503},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4070424437522888},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39171722531318665},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/978-3-642-39206-1_37","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-39206-1_37","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.297.7244","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.297.7244","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.csc.kth.se/~jakobn/research/TowardsUnderstandingPC_ICALP.pdf","raw_type":"text"},{"id":"pmh:oai:iris.uniroma1.it:11573/957567","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/957567","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:lup.lub.lu.se:01e5a064-b88e-4bc8-95e6-1db7cd82e265","is_oa":false,"landing_page_url":"https://lup.lub.lu.se/record/01e5a064-b88e-4bc8-95e6-1db7cd82e265","pdf_url":null,"source":{"id":"https://openalex.org/S4306400536","display_name":"Lund University Publications (Lund University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I187531555","host_organization_name":"Lund University","host_organization_lineage":["https://openalex.org/I187531555"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Lecture Notes in Computer Science; 7965(PART 1), pp 437-448 (2013)","raw_type":"info:eu-repo/semantics/conferencePaper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1518031539","https://openalex.org/W1559980198","https://openalex.org/W1592213313","https://openalex.org/W1965765215","https://openalex.org/W1974070050","https://openalex.org/W1988083342","https://openalex.org/W1990932978","https://openalex.org/W1993216347","https://openalex.org/W2021972008","https://openalex.org/W2036871172","https://openalex.org/W2048051309","https://openalex.org/W2053929306","https://openalex.org/W2056382067","https://openalex.org/W2068871408","https://openalex.org/W2069767473","https://openalex.org/W2071347463","https://openalex.org/W2074834475","https://openalex.org/W2081172416","https://openalex.org/W2084384424","https://openalex.org/W2093126960","https://openalex.org/W2093396771","https://openalex.org/W2098022011","https://openalex.org/W2108637261","https://openalex.org/W2114235518","https://openalex.org/W2122782108","https://openalex.org/W2126420408","https://openalex.org/W2129413084","https://openalex.org/W2132489129","https://openalex.org/W2134253979","https://openalex.org/W2142127354","https://openalex.org/W2164319662","https://openalex.org/W3021939903","https://openalex.org/W3144881883"],"related_works":["https://openalex.org/W4288055874","https://openalex.org/W1662675122","https://openalex.org/W2068071783","https://openalex.org/W2531336559","https://openalex.org/W3013031282","https://openalex.org/W2099785256","https://openalex.org/W2063658344","https://openalex.org/W2165390183","https://openalex.org/W2071347463","https://openalex.org/W2730643286"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":7}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-09-02T00:00:00"}