{"id":"https://openalex.org/W2343759067","doi":"https://doi.org/10.23638/lmcs-13(3:8)2017","title":"Complexity Hierarchies and Higher-order Cons-free Term Rewriting","display_name":"Complexity Hierarchies and Higher-order Cons-free Term Rewriting","publication_year":2017,"publication_date":"2017-08-07","ids":{"openalex":"https://openalex.org/W2343759067","doi":"https://doi.org/10.23638/lmcs-13(3:8)2017","mag":"2343759067"},"language":"en","primary_location":{"id":"doi:10.23638/lmcs-13(3:8)2017","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-13(3:8)2017","pdf_url":"https://lmcs.episciences.org/3847/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/3847/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001880661","display_name":"Cynthia Kop","orcid":"https://orcid.org/0000-0002-6337-2544"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Cynthia Kop","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5024664299","display_name":"Jakob Grue Simonsen","orcid":"https://orcid.org/0000-0002-3488-9392"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jakob Grue Simonsen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001880661"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8314,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.79456878,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"Volume 13, Issue 3","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9954000115394592,"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/T10260","display_name":"Software Engineering Research","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/rewriting","display_name":"Rewriting","score":0.9206345081329346},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.6335842609405518},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5908421277999878},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.4920034110546112},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.4899117350578308},{"id":"https://openalex.org/keywords/determinism","display_name":"Determinism","score":0.44314947724342346},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.43921101093292236},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.430508553981781},{"id":"https://openalex.org/keywords/p","display_name":"P","score":0.42625442147254944},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3807726800441742},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.37621641159057617},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.3638576865196228},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35718315839767456},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30503663420677185},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08040770888328552}],"concepts":[{"id":"https://openalex.org/C154690210","wikidata":"https://www.wikidata.org/wiki/Q1668499","display_name":"Rewriting","level":2,"score":0.9206345081329346},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.6335842609405518},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5908421277999878},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.4920034110546112},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.4899117350578308},{"id":"https://openalex.org/C192183473","wikidata":"https://www.wikidata.org/wiki/Q131133","display_name":"Determinism","level":2,"score":0.44314947724342346},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43921101093292236},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.430508553981781},{"id":"https://openalex.org/C134026603","wikidata":"https://www.wikidata.org/wiki/Q846354","display_name":"P","level":3,"score":0.42625442147254944},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3807726800441742},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.37621641159057617},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3638576865196228},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35718315839767456},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30503663420677185},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08040770888328552},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.23638/lmcs-13(3:8)2017","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-13(3:8)2017","pdf_url":"https://lmcs.episciences.org/3847/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1611.10334","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.10334","pdf_url":"https://arxiv.org/pdf/1611.10334","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":"pmh:oai:pure.atira.dk:openaire_cris_publications/455ebc9b-6981-476b-8663-0b82ad7b294a","is_oa":true,"landing_page_url":"https://curis.ku.dk/portal/da/publications/complexity-hierarchies-and-higherorder-consfree-term-rewriting(455ebc9b-6981-476b-8663-0b82ad7b294a).html","pdf_url":"https://curis.ku.dk/ws/files/189255279/Kop_2017_Complexity_hierarchies.pdf","source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"doi:10.48550/arxiv.1611.10334","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1611.10334","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-journal"},{"id":"mag:3023912086","is_oa":true,"landing_page_url":"https://dblp.uni-trier.de/db/journals/lmcs/lmcs13.html#KopS17","pdf_url":null,"source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Logical Methods in Computer Science","raw_type":null}],"best_oa_location":{"id":"doi:10.23638/lmcs-13(3:8)2017","is_oa":true,"landing_page_url":"https://doi.org/10.23638/lmcs-13(3:8)2017","pdf_url":"https://lmcs.episciences.org/3847/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4918079699","display_name":null,"funder_award_id":"658162","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322928","display_name":"Danmarks Frie Forskningsfond","ror":"https://ror.org/02sptwz63"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2343759067.pdf"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1494177512","https://openalex.org/W1508002867","https://openalex.org/W1533996603","https://openalex.org/W1543209434","https://openalex.org/W1545415328","https://openalex.org/W1581033375","https://openalex.org/W1975808446","https://openalex.org/W1994584977","https://openalex.org/W2053054452","https://openalex.org/W2069792094","https://openalex.org/W2083350000","https://openalex.org/W2098726192","https://openalex.org/W2105438076","https://openalex.org/W2155243135","https://openalex.org/W2269082851","https://openalex.org/W2767652015","https://openalex.org/W2770930245","https://openalex.org/W2788094376","https://openalex.org/W2949239671","https://openalex.org/W2950828120","https://openalex.org/W2953106722"],"related_works":["https://openalex.org/W2970311880","https://openalex.org/W2073028890","https://openalex.org/W4236663059","https://openalex.org/W2199053348","https://openalex.org/W2162177529","https://openalex.org/W2154884611","https://openalex.org/W2026191634","https://openalex.org/W4289670448","https://openalex.org/W2889033124","https://openalex.org/W2073674197"],"abstract_inverted_index":{"Constructor":[0],"rewriting":[1,70,138,166],"systems":[2,98,139,167],"are":[3,18,188],"said":[4],"to":[5,44,60,239,257],"be":[6],"cons-free":[7,39,54,67,97,164],"if,":[8],"roughly,":[9],"constructor":[10],"terms":[11],"in":[12,51,126],"the":[13,21,24,62,72,82,86,111,190,195,234],"right-hand":[14],"sides":[15],"of":[16,20,47,85,194,222,253],"rules":[17,29],"subterms":[19],"left-hand":[22],"sides;":[23],"computational":[25,48],"intuition":[26],"is":[27,108,129],"that":[28,130,209,231],"cannot":[30],"build":[31],"new":[32],"data":[33],"structures.":[34],"In":[35],"programming":[36],"language":[37],"research,":[38],"languages":[40],"have":[41,57,115,168],"been":[42,58,171],"used":[43,59,109],"characterize":[45,61,103],"hierarchies":[46],"complexity":[49,73,128,224],"classes;":[50],"term":[52,69,137,165],"rewriting,":[53],"first-order":[55],"TRSs":[56],"class":[63],"PTIME.":[64],"We":[65,88,228],"investigate":[66],"higher-order":[68],"systems,":[71],"classes":[74,152,225,235],"they":[75],"characterize,":[76],"and":[77,160,177,184],"how":[78],"these":[79],"depend":[80],"on":[81,143],"type":[83,100,155],"order":[84,101,156],"systems.":[87],"prove":[89],"that,":[90],"for":[91,135,153,163,173,220],"every":[92],"K":[93,102,174],"$\\geq$":[94],"1,":[95,176],"left-linear":[96],"with":[99,123,140,178,266],"E$^K$TIME":[104],"if":[105],"unrestricted":[106],"evaluation":[107],"(i.e.,":[110],"system":[112],"does":[113,216],"not":[114,217],"a":[116,254],"fixed":[117],"reduction":[118,144],"strategy).":[119],"The":[120],"main":[121],"difference":[122],"prior":[124,207],"work":[125,205],"implicit":[127,192],"(i)":[131],"our":[132],"results":[133,162,187,208],"hold":[134],"non-orthogonal":[136],"no":[141],"assumptions":[142],"strategy,":[145],"(ii)":[146],"we":[147],"consequently":[148],"obtain":[149],"much":[150],"larger":[151],"each":[154],"(E$^K$TIME":[157],"versus":[158],"EXP$^{K-1}$TIME),":[159],"(iii)":[161],"previously":[169],"only":[170],"obtained":[172],"=":[175,198],"additional":[179],"syntactic":[180,241],"restrictions":[181],"besides":[182],"cons-freeness":[183],"left-linearity.":[185],"Our":[186,204],"among":[189],"first":[191],"characterizations":[193],"hierarchy":[196],"E":[197],"E$^1$TIME":[199],"$\\subsetneq$":[200,202],"E$^2$TIME":[201],"...":[203],"confirms":[206],"having":[210],"full":[211],"non-determinism":[212,232],"(via":[213],"overlapping":[214],"rules)":[215],"directly":[218],"allow":[219],"characterization":[221],"non-deterministic":[223],"like":[226,243],"NE.":[227],"also":[229],"show":[230],"makes":[233],"characterized":[236],"highly":[237],"sensitive":[238],"minor":[240],"changes":[242],"admitting":[244],"product":[245],"types":[246],"or":[247],"non-left-linear":[248],"rules.":[249],"Comment:":[250],"extended":[251],"version":[252],"paper":[255],"submitted":[256],"FSCD":[258],"2016.":[259],"arXiv":[260],"admin":[261],"note:":[262],"substantial":[263],"text":[264],"overlap":[265],"arXiv:1604.08936":[267]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":4}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}