{"id":"https://openalex.org/W2055874330","doi":"https://doi.org/10.1137/0218043","title":"Expressibility and Parallel Complexity","display_name":"Expressibility and Parallel Complexity","publication_year":1989,"publication_date":"1989-06-01","ids":{"openalex":"https://openalex.org/W2055874330","doi":"https://doi.org/10.1137/0218043","mag":"2055874330"},"language":"en","primary_location":{"id":"doi:10.1137/0218043","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0218043","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5053065200","display_name":"Neil Immerman","orcid":"https://orcid.org/0000-0001-6609-5952"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Neil Immerman","raw_affiliation_strings":["YALE UNIVERSITY, New Haven, CT"],"affiliations":[{"raw_affiliation_string":"YALE UNIVERSITY, New Haven, CT","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053065200"],"corresponding_institution_ids":["https://openalex.org/I32971472"],"apc_list":null,"apc_paid":null,"fwci":8.1331,"has_fulltext":false,"cited_by_count":124,"citation_normalized_percentile":{"value":0.98405921,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"18","issue":"3","first_page":"625","last_page":"638"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","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"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","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/T10142","display_name":"Formal Methods in Verification","score":0.9988999962806702,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9987000226974487,"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/iterated-function","display_name":"Iterated function","score":0.7619903683662415},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6880309581756592},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6803101301193237},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.6341515779495239},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.601740300655365},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.5777484774589539},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.577692449092865},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5497928857803345},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5352222919464111},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4971766769886017},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.45072272419929504},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.4355296492576599},{"id":"https://openalex.org/keywords/sentence","display_name":"Sentence","score":0.4294508695602417},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38522106409072876},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36731839179992676}],"concepts":[{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7619903683662415},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6880309581756592},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6803101301193237},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.6341515779495239},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.601740300655365},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.5777484774589539},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.577692449092865},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5497928857803345},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5352222919464111},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4971766769886017},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45072272419929504},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.4355296492576599},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.4294508695602417},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38522106409072876},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36731839179992676},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"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/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/0218043","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0218043","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.57.1834","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.1834","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.umass.edu/~immerman/pub/parallel.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.66.4254","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.66.4254","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.umass.edu/~immerman/pub/parallel.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.6100000143051147,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1591825827","https://openalex.org/W1607100166","https://openalex.org/W1967575173","https://openalex.org/W1970629906","https://openalex.org/W1984581643","https://openalex.org/W1986804393","https://openalex.org/W2027501230","https://openalex.org/W2065251436","https://openalex.org/W2075322882","https://openalex.org/W2088094394","https://openalex.org/W2105505307"],"related_works":["https://openalex.org/W2376029318","https://openalex.org/W2388301251","https://openalex.org/W2013770701","https://openalex.org/W3013941779","https://openalex.org/W1998659141","https://openalex.org/W3195376785","https://openalex.org/W2370435933","https://openalex.org/W138938013","https://openalex.org/W4316469561","https://openalex.org/W2947625790"],"abstract_inverted_index":{"It":[0,75],"is":[1,22,41,64,76,105,133,143],"shown":[2,77],"that":[3,78],"the":[4,23,26,36,44,56,65,84,110,138,146],"time":[5,119],"needed":[6,53],"by":[7,92,123,151],"a":[8,19,30,50,68,121,134,152],"concurrent-read,":[9],"concurrentwrite":[10],"parallel":[11,165],"random":[12],"access":[13],"machine":[14],"(CRAM)":[15],"tocheck":[16],"ifaninput":[17],"has":[18],"certain":[20],"property":[21],"same":[24],"as":[25],"minimal":[27],"depth":[28],"of":[29,35,46,49,61,67,129,137,148],"rstorder":[31],"inductive":[32],"de":[33,81,106],"nition":[34,82],"property.":[37,57],"This":[38],"in":[39],"turn":[40],"equal":[42,116,144],"to":[43,54,108,117,145],"number":[45],"\\\\iterations":[47],"&amp;amp;quot;":[48,96],"rst-order":[51,93,111,167],"sentence":[52],"express":[55],"The":[58],"second":[59],"contribution":[60],"this":[62],"paper":[63],"introduction":[66],"purely":[69],"syntactic":[70],"uniformity":[71],"notion":[72],"for":[73,83],"circuits.":[74],"an":[79],"equivalent":[80],"uniform":[85,102],"circuit":[86],"classes":[87],"AC":[88,103],"i":[89,98],"\ufffdi":[90],"1isgiven":[91],"sentences":[94],"\\\\iterated":[95],"log":[97],"n":[99],"times.":[100],"Similarly,":[101],"0":[104],"ned":[107],"be":[109],"expressible":[112],"properties":[113],"(which":[114],"inturnis":[115],"constant":[118,159],"on":[120],"CRAM":[122,153],"our":[124,130],"main":[125,131],"theorem).":[126],"A":[127],"corollary":[128],"result":[132],"new":[135],"characterization":[136],"Polynomial-Time":[139],"Hierarchy":[140],"(PH):":[141],"PH":[142],"set":[147],"languages":[149],"accepted":[150],"using":[154],"exponentially":[155],"many":[156],"processors":[157],"and":[158],"time.":[160],"Key":[161],"words.":[162],"Computational":[163],"complexity,":[164,166],"expressibility,":[168],"polynomial-time":[169],"hierarchy":[170],"AMS(MOS)":[171],"subject":[172],"classi":[173],"cation.":[174],"68025":[175],"1":[176]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
