{"id":"https://openalex.org/W2163596802","doi":"https://doi.org/10.1051/ita:2000107","title":"Construction of Very Hard Functions for Multiparty Communication Complexity","display_name":"Construction of Very Hard Functions for Multiparty Communication Complexity","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2163596802","doi":"https://doi.org/10.1051/ita:2000107","mag":"2163596802"},"language":"en","primary_location":{"id":"doi:10.1051/ita:2000107","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2000107","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.numdam.org/item/ITA_2000__34_1_61_0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002286397","display_name":"J\u00e1n Ma\u0148uch","orcid":"https://orcid.org/0000-0002-6937-249X"},"institutions":[{"id":"https://openalex.org/I155660961","display_name":"University of Turku","ror":"https://ror.org/05vghhr25","country_code":"FI","type":"education","lineage":["https://openalex.org/I155660961"]},{"id":"https://openalex.org/I183173800","display_name":"Turku Centre for Computer Science","ror":"https://ror.org/00vy7ed73","country_code":"FI","type":"facility","lineage":["https://openalex.org/I130217899","https://openalex.org/I155660961","https://openalex.org/I183173800"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"J\u00e1n Ma\u0148uch","raw_affiliation_strings":["Department of Mathematics and Turku Centre for Computer Science, University of Turku, Turku, Finland; (manuch@cs.utu.fi)","Department of Mathematics and Turku Centre for Computer Science, University of Turku, Turku, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Turku Centre for Computer Science, University of Turku, Turku, Finland; (manuch@cs.utu.fi)","institution_ids":["https://openalex.org/I183173800"]},{"raw_affiliation_string":"Department of Mathematics and Turku Centre for Computer Science, University of Turku, Turku, Finland","institution_ids":["https://openalex.org/I183173800","https://openalex.org/I155660961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002286397"],"corresponding_institution_ids":["https://openalex.org/I155660961","https://openalex.org/I183173800"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.19049521,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"1","first_page":"61","last_page":"75"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.9417321085929871},{"id":"https://openalex.org/keywords/communication-complexity","display_name":"Communication complexity","score":0.670768141746521},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.6436055898666382},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.6318478584289551},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5853962898254395},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5149901509284973},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5055253505706787},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4711044430732727},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44979313015937805},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.41888517141342163},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3880046010017395},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38740605115890503},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36093682050704956},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.059785395860672}],"concepts":[{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.9417321085929871},{"id":"https://openalex.org/C179145077","wikidata":"https://www.wikidata.org/wiki/Q5154130","display_name":"Communication complexity","level":2,"score":0.670768141746521},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.6436055898666382},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.6318478584289551},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5853962898254395},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5149901509284973},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5055253505706787},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4711044430732727},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44979313015937805},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.41888517141342163},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3880046010017395},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38740605115890503},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36093682050704956},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.059785395860672},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1051/ita:2000107","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2000107","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:ITA_2000__34_1_61_0","is_oa":true,"landing_page_url":"http://www.numdam.org/item/ITA_2000__34_1_61_0/","pdf_url":"https://www.numdam.org/item/ITA_2000__34_1_61_0.pdf","source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.28.4131","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.4131","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.tucs.fi/Pub/2000/Journ/jManucha.ps","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:numdam.org:ITA_2000__34_1_61_0","is_oa":true,"landing_page_url":"http://www.numdam.org/item/ITA_2000__34_1_61_0/","pdf_url":"https://www.numdam.org/item/ITA_2000__34_1_61_0.pdf","source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2163596802.pdf","grobid_xml":"https://content.openalex.org/works/W2163596802.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W605043455","https://openalex.org/W1551208484","https://openalex.org/W1998270481","https://openalex.org/W2003007405","https://openalex.org/W2009195096","https://openalex.org/W2023412106","https://openalex.org/W2068422506","https://openalex.org/W2079051917","https://openalex.org/W2079401865","https://openalex.org/W2086814302","https://openalex.org/W2142151475"],"related_works":["https://openalex.org/W2963463650","https://openalex.org/W1524987448","https://openalex.org/W2766148426","https://openalex.org/W4297955154","https://openalex.org/W2101249745","https://openalex.org/W2079051917","https://openalex.org/W1982283204","https://openalex.org/W2565389498","https://openalex.org/W2124096260","https://openalex.org/W2163596802"],"abstract_inverted_index":{"We":[0,89],"consider":[1],"the":[2,10,20,23,33,58,99],"multiparty":[3],"communication":[4,35,62],"model":[5],"defined":[6],"in":[7,19,75],"[4]":[8],"using":[9],"formalism":[11],"from":[12],"[8].":[13],"First,":[14],"we":[15,41],"correct":[16],"an":[17],"inaccuracy":[18],"proof":[21],"of":[22,26,37],"fundamental":[24],"result":[25],"[6]":[27],"providing":[28],"a":[29,38,68,104],"lower":[30],"bound":[31],"on":[32],"nondeterministic":[34,61],"complexity":[36],"function.":[39,107],"Then":[40],"construct":[42],"several":[43],"very":[44,70,87,95,105],"hard":[45,71,96,106],"functions,":[46],"i.e.,":[47],"functions":[48,85,97],"such":[49],"that":[50,82,92],"those":[51],"as":[52,54],"well":[53],"their":[55],"complements":[56],"have":[57],"worst":[59],"possible":[60],"complexity.":[63],"The":[64],"problem":[65],"to":[66],"find":[67],"particular":[69],"function":[72],"was":[73],"proposed":[74],"[7],":[76],"where":[77],"it":[78],"has":[79],"been":[80],"shown":[81],"almost":[83],"all":[84],"are":[86],"hard.":[88],"also":[90],"prove":[91],"combining":[93],"two":[94],"by":[98],"Boolean":[100],"operation":[101],"xor":[102],"gives":[103]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}