{"id":"https://openalex.org/W2912115172","doi":"https://doi.org/10.1007/s00453-021-00915-7","title":"A #SAT Algorithm for Small Constant-Depth Circuits with PTF gates","display_name":"A #SAT Algorithm for Small Constant-Depth Circuits with PTF gates","publication_year":2022,"publication_date":"2022-01-07","ids":{"openalex":"https://openalex.org/W2912115172","doi":"https://doi.org/10.1007/s00453-021-00915-7","mag":"2912115172"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-021-00915-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00453-021-00915-7","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1809.05932","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091672134","display_name":"Swapnam Bajpai","orcid":null},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Swapnam Bajpai","raw_affiliation_strings":["Department of Computer Science and Engineering, IIT Bombay, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, IIT Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048611967","display_name":"Vaibhav Krishan","orcid":"https://orcid.org/0009-0000-0335-1963"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Vaibhav Krishan","raw_affiliation_strings":["Department of Computer Science and Engineering, IIT Bombay, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, IIT Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087309847","display_name":"Deepanshu Kush","orcid":null},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Deepanshu Kush","raw_affiliation_strings":["Department of Mathematics, IIT Bombay, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, IIT Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083072245","display_name":"Nutan Limaye","orcid":"https://orcid.org/0000-0002-0238-1674"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Nutan Limaye","raw_affiliation_strings":["Department of Computer Science and Engineering, IIT Bombay, Mumbai, India","Indian Institute of Technology Bombay, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, IIT Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025305994","display_name":"Srikanth Srinivasan","orcid":"https://orcid.org/0000-0001-6491-124X"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Srikanth Srinivasan","raw_affiliation_strings":["Department of Mathematics, IIT Bombay, Mumbai, India","Indian Institute of Technology Bombay, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, IIT Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5091672134"],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00160113,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"84","issue":"4","first_page":"1132","last_page":"1162"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9995999932289124,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9968000054359436,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9945999979972839,"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/mathematics","display_name":"Mathematics","score":0.7154629826545715},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.7006003856658936},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.6505435705184937},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.64654541015625},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.6089299917221069},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5217698216438293},{"id":"https://openalex.org/keywords/maximum-satisfiability-problem","display_name":"Maximum satisfiability problem","score":0.5078523755073547},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.5051606297492981},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5035189986228943},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4849455654621124},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4609028100967407},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42714887857437134},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1775738000869751},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1577644944190979}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7154629826545715},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.7006003856658936},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.6505435705184937},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.64654541015625},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.6089299917221069},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5217698216438293},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.5078523755073547},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.5051606297492981},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5035189986228943},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4849455654621124},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4609028100967407},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42714887857437134},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1775738000869751},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1577644944190979},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00453-021-00915-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00453-021-00915-7","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1809.05932","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.05932","pdf_url":"https://arxiv.org/pdf/1809.05932","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"doi:10.48550/arxiv.1809.05932","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1809.05932","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:2912115172","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/eccc/eccc25.html#BajpaiKKLS18","pdf_url":null,"source":{"id":"https://openalex.org/S4306509107","display_name":"Electron. Colloquium Comput. Complex.","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":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Electron. Colloquium Comput. Complex.","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1809.05932","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.05932","pdf_url":"https://arxiv.org/pdf/1809.05932","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2756940399","display_name":null,"funder_award_id":"MTR/2017/000909","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"},{"id":"https://openalex.org/G4665680769","display_name":null,"funder_award_id":"MTR/2017/000958","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"}],"funders":[{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1571792361","https://openalex.org/W1862379263","https://openalex.org/W1974632918","https://openalex.org/W2001187993","https://openalex.org/W2003519998","https://openalex.org/W2007121506","https://openalex.org/W2024091095","https://openalex.org/W2026339776","https://openalex.org/W2049136377","https://openalex.org/W2050715481","https://openalex.org/W2062514359","https://openalex.org/W2063836706","https://openalex.org/W2064790310","https://openalex.org/W2083820240","https://openalex.org/W2084194126","https://openalex.org/W2097886040","https://openalex.org/W2124218043","https://openalex.org/W2128524323","https://openalex.org/W2175125908","https://openalex.org/W2178011018","https://openalex.org/W2191626561","https://openalex.org/W2545696445","https://openalex.org/W2610692559","https://openalex.org/W2624881990","https://openalex.org/W2884125338","https://openalex.org/W2912080987","https://openalex.org/W2964321744","https://openalex.org/W3102754027","https://openalex.org/W3108106901"],"related_works":["https://openalex.org/W2952971107","https://openalex.org/W2624881990","https://openalex.org/W302036035","https://openalex.org/W2765993145","https://openalex.org/W1625693084","https://openalex.org/W1544866824","https://openalex.org/W2094783265","https://openalex.org/W2460503887","https://openalex.org/W1601605622","https://openalex.org/W2102477571","https://openalex.org/W2540343126","https://openalex.org/W1880954240","https://openalex.org/W2889078076","https://openalex.org/W1915058039","https://openalex.org/W2002068271","https://openalex.org/W2951586353","https://openalex.org/W2026339776","https://openalex.org/W2952360260","https://openalex.org/W2401055316","https://openalex.org/W3199523595"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}