{"id":"https://openalex.org/W2990947232","doi":"https://doi.org/10.1093/jigpal/jzz078","title":"A restricted second-order logic for non-deterministic poly-logarithmic time","display_name":"A restricted second-order logic for non-deterministic poly-logarithmic time","publication_year":2019,"publication_date":"2019-11-18","ids":{"openalex":"https://openalex.org/W2990947232","doi":"https://doi.org/10.1093/jigpal/jzz078","mag":"2990947232"},"language":"en","primary_location":{"id":"doi:10.1093/jigpal/jzz078","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzz078","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of the IGPL","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1912.00010","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035972346","display_name":"Flavio Ferrarotti","orcid":"https://orcid.org/0000-0003-2278-8233"},"institutions":[{"id":"https://openalex.org/I4210126338","display_name":"Software Competence Center Hagenberg (Austria)","ror":"https://ror.org/02ks3nr96","country_code":"AT","type":"company","lineage":["https://openalex.org/I4210126338"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Flavio Ferrarotti","raw_affiliation_strings":["Software Competence Center Hagenberg 4232, Austria","Sussex Coast College Hastings"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Software Competence Center Hagenberg 4232, Austria","institution_ids":["https://openalex.org/I4210126338"]},{"raw_affiliation_string":"Sussex Coast College Hastings","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014611318","display_name":"Senen Gonz\u00e1les","orcid":null},"institutions":[{"id":"https://openalex.org/I4210126338","display_name":"Software Competence Center Hagenberg (Austria)","ror":"https://ror.org/02ks3nr96","country_code":"AT","type":"company","lineage":["https://openalex.org/I4210126338"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Sen\u00c9n Gonz\u00c1les","raw_affiliation_strings":["Software Competence Center Hagenberg 4232, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Software Competence Center Hagenberg 4232, Austria","institution_ids":["https://openalex.org/I4210126338"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000905974","display_name":"Klaus\u2010Dieter Schewe","orcid":"https://orcid.org/0000-0002-8309-1803"},"institutions":[{"id":"https://openalex.org/I4210158570","display_name":"Zhejiang University-University of Edinburgh Institute","ror":"https://ror.org/04jth1r26","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210158570","https://openalex.org/I76130692","https://openalex.org/I98677209"]},{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Klaus-Dieter Schewe","raw_affiliation_strings":["Zhejiang University, UIUC Institute, Haining 314400, China","(Zhejiang University)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhejiang University, UIUC Institute, Haining 314400, China","institution_ids":["https://openalex.org/I4210158570"]},{"raw_affiliation_string":"(Zhejiang University)","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108553530","display_name":"Jos\u00e9 Mar\u00eda Turull-Torres","orcid":null},"institutions":[{"id":"https://openalex.org/I63181348","display_name":"Universidad Nacional de La Matanza","ror":"https://ror.org/01bmj8t37","country_code":"AR","type":"education","lineage":["https://openalex.org/I63181348"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Jos\u00c9 Mar\u00cda Turull-Torres","raw_affiliation_strings":["Universidad Nacional de La Matanza, Buenos Aires C1093 ABE, Argentina","National University of La Matanza"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad Nacional de La Matanza, Buenos Aires C1093 ABE, Argentina","institution_ids":["https://openalex.org/I63181348"]},{"raw_affiliation_string":"National University of La Matanza","institution_ids":["https://openalex.org/I63181348"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5035972346"],"corresponding_institution_ids":["https://openalex.org/I4210126338"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19130499,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"3","first_page":"389","last_page":"412"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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/T10237","display_name":"Cryptography and Data Security","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"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9995999932289124,"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":0.704211950302124},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5883323550224304},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.5815786123275757},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5379780530929565},{"id":"https://openalex.org/keywords/arity","display_name":"Arity","score":0.482328861951828},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4702174663543701},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4678885042667389},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.45920947194099426},{"id":"https://openalex.org/keywords/descriptive-complexity-theory","display_name":"Descriptive complexity theory","score":0.4496316909790039},{"id":"https://openalex.org/keywords/turing-machine","display_name":"Turing machine","score":0.4278066158294678},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.4152417778968811},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11215734481811523}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.704211950302124},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5883323550224304},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.5815786123275757},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5379780530929565},{"id":"https://openalex.org/C110546421","wikidata":"https://www.wikidata.org/wiki/Q1315869","display_name":"Arity","level":2,"score":0.482328861951828},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4702174663543701},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4678885042667389},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.45920947194099426},{"id":"https://openalex.org/C133142742","wikidata":"https://www.wikidata.org/wiki/Q1200755","display_name":"Descriptive complexity theory","level":3,"score":0.4496316909790039},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.4278066158294678},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.4152417778968811},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11215734481811523},{"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1093/jigpal/jzz078","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzz078","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of the IGPL","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1912.00010","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1912.00010","pdf_url":"https://arxiv.org/pdf/1912.00010","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"mag:2990947232","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1912.00010v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1912.00010","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1912.00010","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1912.00010","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1912.00010","pdf_url":"https://arxiv.org/pdf/1912.00010","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7400000095367432}],"awards":[{"id":"https://openalex.org/G7413203456","display_name":null,"funder_award_id":"I2420-N31","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320323031","display_name":"\u00d6sterreichische Forschungsf\u00f6rderungsgesellschaft","ror":"https://ror.org/028jc0449"},{"id":"https://openalex.org/F4320323033","display_name":"Bundesministerium f\u00fcr Verkehr, Innovation und Technologie","ror":"https://ror.org/04marky29"},{"id":"https://openalex.org/F4320327593","display_name":"Bundesministerium f\u00fcr Digitalisierung und Wirtschaftsstandort","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2990947232.pdf","grobid_xml":"https://content.openalex.org/works/W2990947232.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1234389479","https://openalex.org/W1489366126","https://openalex.org/W1566349547","https://openalex.org/W1889920293","https://openalex.org/W1968490853","https://openalex.org/W1975410968","https://openalex.org/W1980103601","https://openalex.org/W2006396461","https://openalex.org/W2036265926","https://openalex.org/W2036981717","https://openalex.org/W2045583484","https://openalex.org/W2055288944","https://openalex.org/W2065251436","https://openalex.org/W2114577599","https://openalex.org/W2117313088","https://openalex.org/W2169974244","https://openalex.org/W2171280299","https://openalex.org/W2190928263","https://openalex.org/W2409645877","https://openalex.org/W2963628519","https://openalex.org/W4236835455","https://openalex.org/W6634013968","https://openalex.org/W6639314815","https://openalex.org/W6651908102","https://openalex.org/W6659573362","https://openalex.org/W6677246771","https://openalex.org/W6752241625","https://openalex.org/W6948056383"],"related_works":["https://openalex.org/W3000564918","https://openalex.org/W1543965609","https://openalex.org/W2188703919","https://openalex.org/W2057322444","https://openalex.org/W113209803","https://openalex.org/W2152663086","https://openalex.org/W1991188222","https://openalex.org/W1494513799","https://openalex.org/W2038751575","https://openalex.org/W1987288831","https://openalex.org/W2018805361","https://openalex.org/W2531234554","https://openalex.org/W2922213978","https://openalex.org/W2903809398","https://openalex.org/W2097212968","https://openalex.org/W225390579","https://openalex.org/W3046947725","https://openalex.org/W2956865288","https://openalex.org/W2289748219","https://openalex.org/W2776057122"],"abstract_inverted_index":{"Abstract":[0],"We":[1,28,44,246],"introduce":[2],"a":[3,47,79,148,165],"restricted":[4,235],"second-order":[5,12,124,173,215,236],"logic":[6,34,125,174,216,237],"$\\textrm{SO}^{\\textit{plog}}$":[7,65,141,155,195],"for":[8,93],"finite":[9,130,138],"structures":[10],"where":[11],"quantification":[13],"ranges":[14],"over":[15,128,136],"relations":[16],"of":[17,25,32,64,71,102,123,151,159,178,194,199,214],"size":[18,24,230],"at":[19],"most":[20],"poly-logarithmic":[21,107,162,202],"in":[22,41,60,89,105,164,244,250],"the":[23,26,30,53,61,69,87,100,120,152,190,197,200,207,210,218,226],"structure.":[27],"demonstrate":[29],"relevance":[31],"this":[33,248],"and":[35,196,217,233],"complexity":[36],"class":[37,70,101],"by":[38,78,239],"several":[39],"problems":[40,73,103],"database":[42],"theory.":[43],"then":[45],"prove":[46],"Fagin\u2019s":[48,115],"style":[49],"theorem":[50,116],"showing":[51],"that":[52,74,113,119],"Boolean":[54],"queries":[55],"which":[56,117,167],"can":[57,75],"be":[58,76,111],"expressed":[59],"existential":[62,121],"fragment":[63,122],"correspond":[66],"exactly":[67],"to":[68,86,99,146,171,206,225],"decision":[72],"computed":[77],"non-deterministic":[80,106,201],"Turing":[81],"machine":[82],"with":[83],"random":[84],"access":[85],"input":[88],"time":[90,203],"$O((\\log":[91],"n)^k)$":[92],"some":[94],"$k":[95],"\\ge":[96],"0$,":[97],"i.e.":[98],"computable":[104],"time.":[108],"It":[109],"should":[110],"noted":[112],"unlike":[114],"proves":[118],"captures":[126],"NP":[127],"arbitrary":[129],"structures,":[131,139],"our":[132],"result":[133],"only":[134],"holds":[135],"ordered":[137],"since":[140],"is":[142,168],"too":[143],"weak":[144],"as":[145],"define":[147],"total":[149],"order":[150],"domain.":[153],"Nevertheless,":[154],"provides":[156,175],"natural":[157,176],"levels":[158,177,198],"expressibility":[160,179],"within":[161,180],"space":[163],"way":[166],"closely":[169,223],"related":[170],"how":[172],"polynomial":[181],"space.":[182],"Indeed,":[183],"we":[184],"show":[185],"an":[186],"exact":[187],"correspondence":[188,208],"between":[189,209],"quantifier":[191,211],"prefix":[192,212],"classes":[193,213],"hierarchy,":[204],"analogous":[205],"polynomial-time":[219],"hierarchy.":[220],"Our":[221],"work":[222],"relates":[224],"constant":[227],"depth":[228],"quasipolynomial":[229],"AND/OR":[231],"circuits":[232],"corresponding":[234],"defined":[238],"David":[240],"A.":[241],"Mix":[242],"Barrington":[243],"1992.":[245],"explore":[247],"relationship":[249],"detail.":[251]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}