{"id":"https://openalex.org/W2007706420","doi":"https://doi.org/10.1137/0216052","title":"Logspace Hierarchies, Polynomial Time and the Complexity of Fairness Problems Concerning $\\omega $-Machines","display_name":"Logspace Hierarchies, Polynomial Time and the Complexity of Fairness Problems Concerning $\\omega $-Machines","publication_year":1987,"publication_date":"1987-10-01","ids":{"openalex":"https://openalex.org/W2007706420","doi":"https://doi.org/10.1137/0216052","mag":"2007706420"},"language":"en","primary_location":{"id":"doi:10.1137/0216052","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0216052","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/A5109151333","display_name":"Louis E. Rosier","orcid":null},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Louis E. Rosier","raw_affiliation_strings":["University of Texas @ Austin"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas @ Austin","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101878939","display_name":"Hsu\u2010Chun Yen","orcid":"https://orcid.org/0000-0002-1764-1950"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hsu-Chun Yen","raw_affiliation_strings":["Iowa State Univ., Ames and Univ. of Texas, Austin#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Iowa State Univ., Ames and Univ. of Texas, Austin#TAB#","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":3.7326,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.9323234,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"5","first_page":"779","last_page":"807"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9983999729156494,"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/T10142","display_name":"Formal Methods in Verification","score":0.9983999729156494,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.991100013256073,"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":0.9873999953269958,"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/oracle","display_name":"Oracle","score":0.7482206225395203},{"id":"https://openalex.org/keywords/alternation","display_name":"Alternation (linguistics)","score":0.7265639305114746},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.6837185621261597},{"id":"https://openalex.org/keywords/polynomial-hierarchy","display_name":"Polynomial hierarchy","score":0.6378651857376099},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6365516781806946},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5202816128730774},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.5161043405532837},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4626603424549103},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43935126066207886},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.39767956733703613},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3084023594856262}],"concepts":[{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.7482206225395203},{"id":"https://openalex.org/C26826806","wikidata":"https://www.wikidata.org/wiki/Q438358","display_name":"Alternation (linguistics)","level":2,"score":0.7265639305114746},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6837185621261597},{"id":"https://openalex.org/C2776013622","wikidata":"https://www.wikidata.org/wiki/Q2103021","display_name":"Polynomial hierarchy","level":3,"score":0.6378651857376099},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6365516781806946},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5202816128730774},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.5161043405532837},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4626603424549103},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43935126066207886},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.39767956733703613},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3084023594856262},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0216052","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0216052","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.4300000071525574,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W117768600","https://openalex.org/W182448688","https://openalex.org/W185167655","https://openalex.org/W1545342196","https://openalex.org/W1558316751","https://openalex.org/W1561106891","https://openalex.org/W1650804443","https://openalex.org/W1798280647","https://openalex.org/W1975657455","https://openalex.org/W1980326341","https://openalex.org/W1980967952","https://openalex.org/W1982129592","https://openalex.org/W1990558734","https://openalex.org/W1994227664","https://openalex.org/W1997072713","https://openalex.org/W1999647826","https://openalex.org/W2002089154","https://openalex.org/W2011039300","https://openalex.org/W2012539169","https://openalex.org/W2015413218","https://openalex.org/W2022934640","https://openalex.org/W2036265926","https://openalex.org/W2039302045","https://openalex.org/W2065251436","https://openalex.org/W2071367694","https://openalex.org/W2087718129","https://openalex.org/W2090398333","https://openalex.org/W2093454413","https://openalex.org/W2115082275","https://openalex.org/W2165161585","https://openalex.org/W2293273465","https://openalex.org/W2401610261","https://openalex.org/W4241108585","https://openalex.org/W4302339081"],"related_works":["https://openalex.org/W2913217397","https://openalex.org/W270168689","https://openalex.org/W1589381382","https://openalex.org/W2003513300","https://openalex.org/W2086025566","https://openalex.org/W2082636129","https://openalex.org/W2000805093","https://openalex.org/W2075449032","https://openalex.org/W1702487489","https://openalex.org/W2132910148"],"abstract_inverted_index":{"In":[0,157],"this":[1],"paper,":[2],"we":[3,72,130],"define":[4],"a":[5,93],"restricted":[6,121],"logspace":[7,18,36,122,147],"oracle":[8,37,123],"hierarchy":[9,20,124],"which":[10],"turns":[11],"out":[12],"to":[13,16,56,139,170,174,188],"be":[14,140,186],"equivalent":[15],"the":[17,31,35,74,88,114,120,134,146,159,175,183],"alternation":[19,148],"(of":[21,39],"Chandra,":[22],"Kozen":[23],"and":[24,26,42,63,80,111,116],"Stockmeyer)":[25],"thus":[27],"is":[28,85],"contained":[29],"within":[30],"second":[32,115],"level":[33],"of":[34,51,119,145,154,177],"heirarchy":[38],"Ruzzo,":[40],"Simon":[41],"Tompa).":[43],"We":[44],"then":[45],"examine":[46],"problems":[47,103,137,151,196],"concerning":[48,192],"various":[49,143],"types":[50],"\u201cfair\u201d":[52],"computations":[53],"with":[54,92],"respect":[55],"$\\omega":[57,64,78,81],"$-Finite":[58],"State":[59],"Machines":[60,67],"($\\omega":[61,68],"$-FSM\u2019s)":[62],"$-One":[65],"Counter":[66],"$-1CM\u2019s).":[69],"For":[70],"example,":[71],"consider":[73],"nonemptiness":[75,160],"problem":[76,161],"for":[77,109,142,165],"$-FSM\u2019s":[79],"$-1CM\u2019s":[82],"where":[83],"acceptance":[84],"defined":[86],"in":[87],"usual":[89],"fashion,":[90],"but":[91,113],"fairness":[94,163,195],"constraint":[95],"imposed":[96],"on":[97],"accepting":[98],"computations.":[99],"Our":[100],"results":[101,184,191],"yield":[102],"that":[104,197],"are":[105,133,152],"complete":[106,141],"not":[107],"only":[108],"LOGSPACE":[110],"PTIME":[112],"third":[117],"levels":[118,144],"as":[125,129],"well.":[126],"As":[127],"far":[128],"know,":[131],"these":[132],"first":[135],"natural":[136],"shown":[138,169],"hierarchy.":[149],"The":[150],"also":[153],"independent":[155],"interest.":[156],"fact,":[158],"(with":[162],"constraints)":[164],"w-machines":[166],"has":[167],"been":[168],"have":[171],"immediate":[172],"applications":[173],"verification":[176],"concurrent":[178],"finite":[179],"state":[180],"programs.":[181],"Furthermore,":[182],"can":[185],"used":[187],"strengthen":[189],"known":[190],"some":[193],"related":[194],"involve":[198],"temporal":[199],"logic":[200],"(e.g.":[201],"model":[202],"checking).":[203]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}