{"id":"https://openalex.org/W2115706866","doi":"https://doi.org/10.1109/sfcs.2003.1238216","title":"Separating the power of monotone span programs over different fields","display_name":"Separating the power of monotone span programs over different fields","publication_year":2004,"publication_date":"2004-03-01","ids":{"openalex":"https://openalex.org/W2115706866","doi":"https://doi.org/10.1109/sfcs.2003.1238216","mag":"2115706866"},"language":"en","primary_location":{"id":"doi:10.1109/sfcs.2003.1238216","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sfcs.2003.1238216","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.","raw_type":"proceedings-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/A5031372016","display_name":"Amos Beimel","orcid":"https://orcid.org/0000-0002-6572-4195"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"A. Beimel","raw_affiliation_strings":["Dept. of Computer Science, Ben-Gurion University, Beer-Sheva, Israel","Department of Computer Science, Ben Gurion University, Beer Sheva, Israel"],"affiliations":[{"raw_affiliation_string":"Dept. of Computer Science, Ben-Gurion University, Beer-Sheva, Israel","institution_ids":["https://openalex.org/I124227911"]},{"raw_affiliation_string":"Department of Computer Science, Ben Gurion University, Beer Sheva, Israel","institution_ids":["https://openalex.org/I124227911"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088801384","display_name":"Enav Weinreb","orcid":null},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"E. Weinreb","raw_affiliation_strings":["Dept. of Computer Science, Ben-Gurion University, Beer-Sheva, Israel","Department of Computer Science, Ben Gurion University, Beer Sheva, Israel"],"affiliations":[{"raw_affiliation_string":"Dept. of Computer Science, Ben-Gurion University, Beer-Sheva, Israel","institution_ids":["https://openalex.org/I124227911"]},{"raw_affiliation_string":"Department of Computer Science, Ben Gurion University, Beer Sheva, Israel","institution_ids":["https://openalex.org/I124227911"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5031372016"],"corresponding_institution_ids":["https://openalex.org/I124227911"],"apc_list":null,"apc_paid":null,"fwci":1.8501,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.88001617,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"1592","issue":null,"first_page":"428","last_page":"501"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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/T10237","display_name":"Cryptography and Data Security","score":0.9997000098228455,"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":0.9993000030517578,"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/monotone-polygon","display_name":"Monotone polygon","score":0.6730892658233643},{"id":"https://openalex.org/keywords/secret-sharing","display_name":"Secret sharing","score":0.6632839441299438},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6403297185897827},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6247470378875732},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5385139584541321},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5348250865936279},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.5220589637756348},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.49642711877822876},{"id":"https://openalex.org/keywords/secure-multi-party-computation","display_name":"Secure multi-party computation","score":0.48548629879951477},{"id":"https://openalex.org/keywords/span","display_name":"Span (engineering)","score":0.4784807562828064},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47418078780174255},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.47151103615760803},{"id":"https://openalex.org/keywords/linear-span","display_name":"Linear span","score":0.47066983580589294},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.46525293588638306},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40611007809638977},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.33570659160614014},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20192846655845642},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19027739763259888},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06872835755348206}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6730892658233643},{"id":"https://openalex.org/C3087436","wikidata":"https://www.wikidata.org/wiki/Q1386603","display_name":"Secret sharing","level":3,"score":0.6632839441299438},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6403297185897827},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6247470378875732},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5385139584541321},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5348250865936279},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.5220589637756348},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.49642711877822876},{"id":"https://openalex.org/C18396474","wikidata":"https://www.wikidata.org/wiki/Q2465888","display_name":"Secure multi-party computation","level":3,"score":0.48548629879951477},{"id":"https://openalex.org/C2778753569","wikidata":"https://www.wikidata.org/wiki/Q1960395","display_name":"Span (engineering)","level":2,"score":0.4784807562828064},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47418078780174255},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.47151103615760803},{"id":"https://openalex.org/C133226019","wikidata":"https://www.wikidata.org/wiki/Q209812","display_name":"Linear span","level":2,"score":0.47066983580589294},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.46525293588638306},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40611007809638977},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33570659160614014},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20192846655845642},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19027739763259888},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06872835755348206},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C147176958","wikidata":"https://www.wikidata.org/wiki/Q77590","display_name":"Civil engineering","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/sfcs.2003.1238216","is_oa":false,"landing_page_url":"https://doi.org/10.1109/sfcs.2003.1238216","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.218.3640","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.3640","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.bgu.ac.il/~beimel/Papers/sepJournal.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.6.2825","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.2825","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.bgu.ac.il/~weinrebe/Papers/BW.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.78.4591","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.78.4591","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.bgu.ac.il/~weinrebe/Papers/BW.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.80.8600","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.80.8600","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.bgu.ac.il/~beimel/Papers/BW.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W14085832","https://openalex.org/W83612273","https://openalex.org/W247697463","https://openalex.org/W1531592115","https://openalex.org/W1550421702","https://openalex.org/W1551614270","https://openalex.org/W1556155774","https://openalex.org/W1583834646","https://openalex.org/W1984242286","https://openalex.org/W1995365759","https://openalex.org/W2018302254","https://openalex.org/W2020709665","https://openalex.org/W2021238854","https://openalex.org/W2070678975","https://openalex.org/W2071846104","https://openalex.org/W2082002555","https://openalex.org/W2088023978","https://openalex.org/W2097407854","https://openalex.org/W2120551550","https://openalex.org/W2133209493","https://openalex.org/W2136687801","https://openalex.org/W2141420453","https://openalex.org/W2169672310","https://openalex.org/W2340787257","https://openalex.org/W2571456248","https://openalex.org/W2610884651","https://openalex.org/W2912956481","https://openalex.org/W2970097841","https://openalex.org/W3029441447","https://openalex.org/W4229606576","https://openalex.org/W4237031071","https://openalex.org/W4238591275","https://openalex.org/W6633155404","https://openalex.org/W6633290222","https://openalex.org/W6635170281","https://openalex.org/W6655049239","https://openalex.org/W6662105567","https://openalex.org/W6698135423"],"related_works":["https://openalex.org/W2397857137","https://openalex.org/W2083084382","https://openalex.org/W1557783852","https://openalex.org/W2768332800","https://openalex.org/W2188298058","https://openalex.org/W3214129216","https://openalex.org/W2129756153","https://openalex.org/W2006088653","https://openalex.org/W1474916271","https://openalex.org/W3119163369"],"abstract_inverted_index":{"Monotone":[0],"span":[1,47,59,101],"programs":[2,60,102],"are":[3,10,40,147,166],"a":[4,71,95,104,134],"linear-algebraic":[5],"model":[6],"of":[7,32,45,57,64,85,122,136],"computation.":[8],"They":[9],"equivalent":[11],"to":[12],"linear":[13,137,150,170],"secret":[14,138,151,163,171],"sharing":[15,139,152,164,172],"schemes":[16,140,165],"and":[17,23,87,125,144],"have":[18],"various":[19],"applications":[20],"in":[21,35,106,115,142],"cryptography":[22],"complexity.":[24],"A":[25],"fundamental":[26],"question":[27],"is":[28,67],"how":[29],"the":[30,33,37,43,46,55],"choice":[31],"field":[34],"which":[36],"algebraic":[38],"operations":[39],"performed":[41],"effects":[42],"power":[44,56],"program.":[48],"In":[49,154],"this":[50,91,156],"paper":[51],"we":[52,69,93,129],"prove":[53,94],"that":[54,131,161],"monotone":[58,100],"over":[61],"finite":[62],"fields":[63,77],"different":[65,79],"characteristics":[66],"incomparable;":[68],"show":[70,130],"super-polynomial":[72,96],"separation":[73],"between":[74],"any":[75,159],"two":[76],"with":[78],"characteristics,":[80],"answering":[81,118],"an":[82,119],"open":[83,120],"problem":[84,121],"Pudlak":[86],"Sgall":[88],"(1998).":[89],"Using":[90],"result":[92],"lower":[97],"bound":[98],"for":[99,103],"function":[105],"uniform":[107],"-":[108],"/spl":[109,116],"Nscr/;/spl":[110],"Cscr/;/sup":[111],"2/":[112],"(and":[113],"therefore":[114],"Pscr/;),":[117],"Babai,":[123],"Wigderson,":[124],"Gal":[126],"(1999).":[127],"Finally,":[128],"quasi-linear":[132],"schemes,":[133],"generalization":[135],"introduced":[141],"Beimel":[143],"Ishai":[145],"(2001),":[146],"stronger":[148],"than":[149,169],"schemes.":[153,173],"particular,":[155],"proves,":[157],"without":[158],"assumptions,":[160],"non-linear":[162],"more":[167],"efficient":[168]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}