{"id":"https://openalex.org/W2139932807","doi":"https://doi.org/10.1109/tc.1986.1676783","title":"New Classes for Parallel Complexity: A Study of Unification and Other Complete Problems for P","display_name":"New Classes for Parallel Complexity: A Study of Unification and Other Complete Problems for P","publication_year":1986,"publication_date":"1986-05-01","ids":{"openalex":"https://openalex.org/W2139932807","doi":"https://doi.org/10.1109/tc.1986.1676783","mag":"2139932807"},"language":"en","primary_location":{"id":"doi:10.1109/tc.1986.1676783","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1986.1676783","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","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/A5003340402","display_name":"Jeffrey Scott Vitter","orcid":"https://orcid.org/0000-0001-7970-6118"},"institutions":[{"id":"https://openalex.org/I73544541","display_name":"Mathematical Sciences Research Institute","ror":"https://ror.org/05hs5r386","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I73544541"]},{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Vitter","raw_affiliation_strings":["Mathematical Sciences Research Institute","Mathematical Sciences Research Institute, Berkeley, CA, USA","Department of Computer Science, Brown University, Providence, RI, USA"],"affiliations":[{"raw_affiliation_string":"Mathematical Sciences Research Institute","institution_ids":["https://openalex.org/I73544541"]},{"raw_affiliation_string":"Mathematical Sciences Research Institute, Berkeley, CA, USA","institution_ids":["https://openalex.org/I73544541"]},{"raw_affiliation_string":"Department of Computer Science, Brown University, Providence, RI, USA","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040047368","display_name":"Simons","orcid":null},"institutions":[{"id":"https://openalex.org/I196272386","display_name":"Providence College","ror":"https://ror.org/00rxpqe74","country_code":"US","type":"education","lineage":["https://openalex.org/I196272386"]},{"id":"https://openalex.org/I53118340","display_name":"Rhode Island College","ror":"https://ror.org/01k5gt570","country_code":"US","type":"education","lineage":["https://openalex.org/I53118340"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Simons","raw_affiliation_strings":["Department of Mathematics and Computer Science, Rhode Island College, Providence, RI, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Rhode Island College, Providence, RI, USA","institution_ids":["https://openalex.org/I53118340","https://openalex.org/I196272386"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003340402"],"corresponding_institution_ids":["https://openalex.org/I27804330","https://openalex.org/I73544541"],"apc_list":null,"apc_paid":null,"fwci":11.6174,"has_fulltext":false,"cited_by_count":82,"citation_normalized_percentile":{"value":0.98472263,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"C-35","issue":"5","first_page":"403","last_page":"418"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","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/T10126","display_name":"Logic, programming, and type systems","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/T11567","display_name":"semigroups and automata theory","score":0.9997000098228455,"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/T11269","display_name":"Algorithms and Data Compression","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"}}],"keywords":[{"id":"https://openalex.org/keywords/parallelizable-manifold","display_name":"Parallelizable manifold","score":0.9158556461334229},{"id":"https://openalex.org/keywords/prolog","display_name":"Prolog","score":0.8078643679618835},{"id":"https://openalex.org/keywords/unification","display_name":"Unification","score":0.7537754774093628},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6986495852470398},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5631213188171387},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.42497098445892334},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4229312241077423},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4229244589805603},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.39201220870018005},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.328345388174057},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.31393593549728394},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2851409614086151}],"concepts":[{"id":"https://openalex.org/C148047603","wikidata":"https://www.wikidata.org/wiki/Q1014612","display_name":"Parallelizable manifold","level":2,"score":0.9158556461334229},{"id":"https://openalex.org/C81721847","wikidata":"https://www.wikidata.org/wiki/Q163468","display_name":"Prolog","level":2,"score":0.8078643679618835},{"id":"https://openalex.org/C96146094","wikidata":"https://www.wikidata.org/wiki/Q609057","display_name":"Unification","level":2,"score":0.7537754774093628},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6986495852470398},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5631213188171387},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.42497098445892334},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4229312241077423},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4229244589805603},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.39201220870018005},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.328345388174057},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.31393593549728394},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2851409614086151},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.1986.1676783","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1986.1676783","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W10131964","https://openalex.org/W32343738","https://openalex.org/W160157518","https://openalex.org/W1513400187","https://openalex.org/W1530974209","https://openalex.org/W1655990431","https://openalex.org/W1836810876","https://openalex.org/W1967575173","https://openalex.org/W1974040526","https://openalex.org/W1979641885","https://openalex.org/W1982347904","https://openalex.org/W1982801224","https://openalex.org/W1985592215","https://openalex.org/W1992520783","https://openalex.org/W2011039300","https://openalex.org/W2011692114","https://openalex.org/W2017387872","https://openalex.org/W2020007061","https://openalex.org/W2054924988","https://openalex.org/W2061739322","https://openalex.org/W2085467310","https://openalex.org/W2087489294","https://openalex.org/W2089828587","https://openalex.org/W2148043549","https://openalex.org/W2166822586","https://openalex.org/W4213232664","https://openalex.org/W4251271324"],"related_works":["https://openalex.org/W4285069850","https://openalex.org/W2891970004","https://openalex.org/W4240963716","https://openalex.org/W1996916724","https://openalex.org/W1974634278","https://openalex.org/W1596637634","https://openalex.org/W2321918740","https://openalex.org/W2392892093","https://openalex.org/W1516362967","https://openalex.org/W4205459073"],"abstract_inverted_index":{"Previous":[0],"theoretical":[1],"work":[2],"in":[3,20,54,120,130,177,180,185,203],"computational":[4],"complexity":[5,40,162],"has":[6],"suggested":[7],"that":[8,45,59],"any":[9],"problem":[10],"which":[11],"is":[12,17,29,168,173,198],"log-space":[13],"complete":[14,61],"for":[15,63,200],"P":[16,64,107,139],"not":[18,24,30],"likely":[19],"NC,":[21],"and":[22,43,75,94,111,118,132,165,184],"thus":[23],"parallelizable.":[25,80],"In":[26],"practice,":[27],"this":[28,35,55],"the":[31,47,114,121,125,204],"case.":[32],"To":[33],"resolve":[34],"paradox,":[36],"we":[37,52],"introduce":[38],"new":[39,160],"classes":[41,163],"PC":[42,131,164],"PC*":[44],"capture":[46],"practical":[48],"notion":[49],"of":[50,67,116,124,138,150,196],"parallelizability":[51],"discuss":[53],"paper.":[56],"We":[57],"show":[58],"foqur":[60],"problems":[62,128],"(nonsparse":[65],"versions":[66],"unification,":[68],"path":[69],"system":[70],"accessibility,":[71],"monotone":[72],"circuit":[73],"value,":[74],"ordered":[76],"depth-first":[77],"search)":[78],"are":[79,86,113,129,156],"That":[81],"is,":[82],"their":[83,143],"running":[84,145],"times":[85,146],"O(E":[87],"+":[88,96],"V)":[89],"on":[90,100],"a":[91,148,174],"sequential":[92,144],"RAM":[93,105],"O(E/P":[95],"V":[97,110],"log":[98],"P)":[99],"an":[101,135],"EXCLUSIVE-READ":[102],"EXCLUSIVE-WRITE":[103],"Parallel":[104],"with":[106],"processors":[108],"where":[109],"E":[112],"numbers":[115],"vertices":[117],"edges":[119],"inputed":[122],"instance":[123],"problem.":[126],"These":[127],"PC*,":[133],"since":[134],"appropriate":[136],"choice":[137],"can":[140],"speed":[141],"up":[142],"by":[147],"factor":[149],"\u03bc(P).":[151],"Several":[152],"interesting":[153],"open":[154],"questions":[155],"raised":[157],"regarding":[158],"these":[159],"parallel":[161,194],"PC*.":[166],"Unification":[167],"particularly":[169],"important":[170],"because":[171],"it":[172],"basic":[175],"operation":[176],"theorem":[178],"proving,":[179],"type":[181],"inference":[182],"algorithms,":[183],"logic":[186],"programming":[187],"languages":[188],"such":[189],"as":[190],"Prolog.":[191],"A":[192],"fast":[193],"implementation":[195],"Prolog":[197],"needed":[199],"software":[201],"development":[202],"Fifth":[205],"Generation":[206],"project.":[207]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}