{"id":"https://openalex.org/W2000032236","doi":"https://doi.org/10.1142/s0129626492000441","title":"CONSTRUCTING AN EXACT PARITY BASE IS IN <font>RNC</font><sup>2</sup>","display_name":"CONSTRUCTING AN EXACT PARITY BASE IS IN <font>RNC</font><sup>2</sup>","publication_year":1992,"publication_date":"1992-12-01","ids":{"openalex":"https://openalex.org/W2000032236","doi":"https://doi.org/10.1142/s0129626492000441","mag":"2000032236"},"language":"en","primary_location":{"id":"doi:10.1142/s0129626492000441","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129626492000441","pdf_url":null,"source":{"id":"https://openalex.org/S18360026","display_name":"Parallel Processing Letters","issn_l":"0129-6264","issn":["0129-6264","1793-642X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Processing Letters","raw_type":"journal-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/A5012585989","display_name":"Giulia Galbiati","orcid":null},"institutions":[{"id":"https://openalex.org/I25217355","display_name":"University of Pavia","ror":"https://ror.org/00s6t1f81","country_code":"IT","type":"education","lineage":["https://openalex.org/I25217355"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. GALBIATI","raw_affiliation_strings":["Dipartimento di Informatica e Sistemistica, Universit\u00e0 di Pavia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica e Sistemistica, Universit\u00e0 di Pavia, Italy","institution_ids":["https://openalex.org/I25217355"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053677027","display_name":"Francesco Maffioli","orcid":null},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"F. MAFFIOLI","raw_affiliation_strings":["Dipartimento di Elettronica e Informazione, Politecnico di Milano, Italy","Dipartimento di Elettronica e Informazione , Politecnico di Milano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica e Informazione, Politecnico di Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"Dipartimento di Elettronica e Informazione , Politecnico di Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1105,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.80612557,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"02","issue":"04","first_page":"301","last_page":"309"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9998000264167786,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9994000196456909,"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":0.7736077308654785},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.7150275111198425},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.5984923243522644},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5824198126792908},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5793757438659668},{"id":"https://openalex.org/keywords/parity","display_name":"Parity (physics)","score":0.5434250831604004},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.5224577188491821},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.49384623765945435},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.432169646024704}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7736077308654785},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.7150275111198425},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.5984923243522644},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5824198126792908},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5793757438659668},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.5434250831604004},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.5224577188491821},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.49384623765945435},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.432169646024704},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129626492000441","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129626492000441","pdf_url":null,"source":{"id":"https://openalex.org/S18360026","display_name":"Parallel Processing Letters","issn_l":"0129-6264","issn":["0129-6264","1793-642X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Processing Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2058299944","https://openalex.org/W4323360720","https://openalex.org/W2888918612","https://openalex.org/W1550144461","https://openalex.org/W4233892543","https://openalex.org/W2783959783","https://openalex.org/W2602164040","https://openalex.org/W2166285859","https://openalex.org/W2037206237","https://openalex.org/W4310658774"],"abstract_inverted_index":{"In":[0],"this":[1],"work":[2],"we":[3],"address":[4],"the":[5,13,16,20,51,86,100,126,149,158,161,182,191],"parallel":[6,52,151],"complexity":[7,53,152],"of":[8,15,19,22,26,70,74,92,104,114,139,144,155,160,163,167,181,184,187,193],"two":[9,194],"combinatorial":[10],"problems,":[11,106,141],"specifically":[12],"problems":[14,48],"existence":[17],"and":[18,77],"construction":[21,162,183],"a":[23,35,66,89,134,164,171,185],"parity":[24,30,42],"base":[25,31,186],"preassigned":[27,168,188],"weight":[28,169],"(exact":[29],"for":[32],"short)":[33],"in":[34,50,83,130,170,177,190],"0-1":[36,115,172,195],"weighted,":[37],"represented":[38,197],"matroid,":[39],"subject":[40],"to":[41,85,119,148],"conditions.":[43],"We":[44,96],"prove":[45],"that":[46,99,180],"these":[47,105,140,156],"lie":[49],"class":[54],"RNC":[55,120],"2":[56,121],",":[57,122],"i.e.":[58],"they":[59],"are":[60,128,143,157],"solvable":[61],"with":[62,111],"one-sided":[63],"error":[64],"by":[65],"logspace":[67],"uniform":[68],"family":[69],"bounded":[71],"fan-in":[72],"circuits":[73],"polynomial":[75,90],"size":[76],"quadratic":[78],"logarithmic":[79],"depth":[80],"which":[81,142],"receive,":[82],"addition":[84],"problem":[87,159],"input,":[88],"number":[91],"random":[93],"input":[94],"bits.":[95],"also":[97,117],"show":[98],"more":[101],"general":[102],"cases":[103,138],"defined":[107],"over":[108],"matroids":[109],"weighted":[110,173,196],"integral":[112],"instead":[113],"weights,":[116],"belong":[118,147],"as":[123,125],"long":[124],"weights":[127],"given":[129],"unary":[131],"notation.":[132],"As":[133],"consequence":[135],"some":[136],"special":[137],"independent":[145],"interest,":[146],"same":[150],"class:":[153],"examples":[154],"perfect":[165],"matching":[166],"graph,":[174],"recently":[175],"addressed":[176],"[1],":[178],"or":[179],"weight,":[189],"intersection":[192],"matroids.":[198]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}