{"id":"https://openalex.org/W1533271350","doi":"https://doi.org/10.1007/978-3-642-22993-0_11","title":"Verifying Proofs in Constant Depth","display_name":"Verifying Proofs in Constant Depth","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1533271350","doi":"https://doi.org/10.1007/978-3-642-22993-0_11","mag":"1533271350"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-22993-0_11","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-22993-0_11","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":"book-chapter","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, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Informatik, Leibniz Universit\u00e4t Hannover, Germany","institution_ids":["https://openalex.org/I114112103"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056318386","display_name":"Samir Datta","orcid":"https://orcid.org/0000-0003-2196-2308"},"institutions":[{"id":"https://openalex.org/I19149307","display_name":"Chennai Mathematical Institute","ror":"https://ror.org/04zp24820","country_code":"IN","type":"education","lineage":["https://openalex.org/I19149307"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Samir Datta","raw_affiliation_strings":["Chennai Mathematical Institute, India"],"affiliations":[{"raw_affiliation_string":"Chennai Mathematical Institute, India","institution_ids":["https://openalex.org/I19149307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020709378","display_name":"Meena Mahajan","orcid":"https://orcid.org/0000-0002-9116-4398"},"institutions":[{"id":"https://openalex.org/I59611059","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05078rg59","country_code":"IN","type":"facility","lineage":["https://openalex.org/I59611059"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Meena Mahajan","raw_affiliation_strings":["Institute of Mathematical Sciences, Chennai, India"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematical Sciences, Chennai, India","institution_ids":["https://openalex.org/I59611059"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055589477","display_name":"Gido Scharfenberger-Fabian","orcid":null},"institutions":[{"id":"https://openalex.org/I36522303","display_name":"Universit\u00e4t Greifswald","ror":"https://ror.org/00r1edq15","country_code":"DE","type":"education","lineage":["https://openalex.org/I36522303"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gido Scharfenberger-Fabian","raw_affiliation_strings":["Institut f\u00fcr Mathematik und Informatik, Ernst-Moritz-Arndt-Universit\u00e4t, Greifswald, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik und Informatik, Ernst-Moritz-Arndt-Universit\u00e4t, Greifswald, Germany","institution_ids":["https://openalex.org/I36522303"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053184300","display_name":"Karteek Sreenivasaiah","orcid":"https://orcid.org/0000-0001-7396-3383"},"institutions":[{"id":"https://openalex.org/I59611059","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05078rg59","country_code":"IN","type":"facility","lineage":["https://openalex.org/I59611059"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Karteek Sreenivasaiah","raw_affiliation_strings":["Institute of Mathematical Sciences, Chennai, India"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematical Sciences, Chennai, India","institution_ids":["https://openalex.org/I59611059"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081736632","display_name":"Michael E. Thomas","orcid":"https://orcid.org/0009-0004-2121-6983"},"institutions":[{"id":"https://openalex.org/I4210162756","display_name":"TWT GmbH Science & Innovation (Germany)","ror":"https://ror.org/05dfxpw18","country_code":"DE","type":"company","lineage":["https://openalex.org/I4210162756"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael Thomas","raw_affiliation_strings":["TWT GmbH, Neuhausen a. d. F., Germany"],"affiliations":[{"raw_affiliation_string":"TWT GmbH, Neuhausen a. d. F., Germany","institution_ids":["https://openalex.org/I4210162756"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008982209","display_name":"Heribert Vollmer","orcid":"https://orcid.org/0000-0002-9292-1960"},"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":false,"raw_author_name":"Heribert Vollmer","raw_affiliation_strings":["Institut f\u00fcr Theoretische Informatik, Leibniz Universit\u00e4t Hannover, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Informatik, Leibniz Universit\u00e4t Hannover, Germany","institution_ids":["https://openalex.org/I114112103"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5042128349"],"corresponding_institution_ids":["https://openalex.org/I114112103"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.5797,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.79133226,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"84","last_page":"95"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.9937999844551086,"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":0.9934999942779541,"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/computer-science","display_name":"Computer science","score":0.7939174175262451},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7721120715141296},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.7364383339881897},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4054163098335266},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3407602310180664},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3349760174751282},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1568613052368164},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1187187135219574}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7939174175262451},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7721120715141296},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.7364383339881897},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4054163098335266},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3407602310180664},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3349760174751282},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1568613052368164},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1187187135219574},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-22993-0_11","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-22993-0_11","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","score":0.6399999856948853,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W41330591","https://openalex.org/W1490189322","https://openalex.org/W1517585663","https://openalex.org/W1524807471","https://openalex.org/W1984459117","https://openalex.org/W1988083342","https://openalex.org/W1989692246","https://openalex.org/W1993729573","https://openalex.org/W1996660205","https://openalex.org/W2008718608","https://openalex.org/W2010873187","https://openalex.org/W2021469124","https://openalex.org/W2024450183","https://openalex.org/W2046812405","https://openalex.org/W2059785423","https://openalex.org/W2066938865","https://openalex.org/W2087012565","https://openalex.org/W2098308941","https://openalex.org/W2110761203","https://openalex.org/W2128632000","https://openalex.org/W2170981586","https://openalex.org/W2963771155","https://openalex.org/W2988890240"],"related_works":["https://openalex.org/W4394650907","https://openalex.org/W154364797","https://openalex.org/W4254119641","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W2576399385","https://openalex.org/W2963408011","https://openalex.org/W4236324517","https://openalex.org/W1586813864"],"abstract_inverted_index":null,"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
