{"id":"https://openalex.org/W7148340641","doi":"https://doi.org/10.48550/arxiv.2604.00591","title":"On the average-case complexity landscape for Tensor-Isomorphism-complete problems over finite fields","display_name":"On the average-case complexity landscape for Tensor-Isomorphism-complete problems over finite fields","publication_year":2026,"publication_date":"2026-04-01","ids":{"openalex":"https://openalex.org/W7148340641","doi":"https://doi.org/10.48550/arxiv.2604.00591"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.00591","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00591","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.00591","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132763863","display_name":"Tiange Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Tiange","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132769060","display_name":"Yinan Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Yinan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100948185","display_name":"Youming Qiao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qiao, Youming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132824672","display_name":"Dacheng Tao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tao, Dacheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5132766283","display_name":"Yingjie Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Yingjie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.27480000257492065,"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"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.27480000257492065,"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"}},{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.2581000030040741,"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/T11130","display_name":"Coding theory and cryptography","score":0.1589999943971634,"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/isomorphism","display_name":"Isomorphism (crystallography)","score":0.6416000127792358},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.505299985408783},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45989999175071716},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.42399999499320984},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.39419999718666077},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.3815999925136566},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.33340001106262207},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.3285999894142151},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.3199999928474426}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6492999792098999},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.6416000127792358},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.505299985408783},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45989999175071716},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.42399999499320984},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.39419999718666077},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3815999925136566},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35089999437332153},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.33340001106262207},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.3199999928474426},{"id":"https://openalex.org/C1680195","wikidata":"https://www.wikidata.org/wiki/Q2296021","display_name":"Tensor algebra","level":5,"score":0.31850001215934753},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C61665672","wikidata":"https://www.wikidata.org/wiki/Q303100","display_name":"Graph isomorphism","level":4,"score":0.30230000615119934},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2782000005245209},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.2660999894142151},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.2637999951839447},{"id":"https://openalex.org/C149488123","wikidata":"https://www.wikidata.org/wiki/Q17098730","display_name":"Matrix analysis","level":3,"score":0.25949999690055847},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2563999891281128},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.00591","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00591","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.00591","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.00591","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0,29],"Grochow":[1],"and":[2,16,22,49,74,86,208,215,222],"Qiao":[3],"(SIAM":[4],"J.":[5],"Comput.,":[6],"2021),":[7],"the":[8,59,93,141,163,201,216],"complexity":[9],"class":[10],"Tensor":[11],"Isomorphism":[12],"(TI)":[13],"was":[14],"introduced":[15],"isomorphism":[17,73,95,111,154],"problems":[18,39],"for":[19,36,71,92,109,149,171],"groups,":[20],"algebras,":[21],"polynomials":[23],"were":[24],"shown":[25],"to":[26,105,161,176,198],"be":[27],"TI-complete.":[28],"this":[30],"paper,":[31],"we":[32,65,196],"study":[33],"average-case":[34,68,89,114,142],"algorithms":[35,70,108,170,180],"several":[37],"TI-complete":[38,145,172],"over":[40,189],"finite":[41,60,190],"fields,":[42],"including":[43],"algebra":[44,72,110],"isomorphism,":[45],"matrix":[46,75,187],"code":[47,76],"conjugacy,":[48],"$4$-tensor":[50,94],"isomorphism.":[51],"Our":[52,156],"main":[53,157],"results":[54,135],"are":[55],"as":[56,205],"follows.":[57],"Over":[58],"field":[61],"of":[62,84,102,126,140,144,166,220],"order":[63],"$q$,":[64],"devise":[66],"(1)":[67],"polynomial-time":[69,90],"conjugacy":[77],"that":[78,96],"succeed":[79],"in":[80,98,117,185,206],"a":[81,99,123,137],"$1/\u0398(q)$":[82],"fraction":[83,101,125],"inputs":[85,127],"(2)":[87],"an":[88],"algorithm":[91],"succeeds":[97],"$1/q^{\u0398(1)}$":[100],"inputs.":[103],"Prior":[104],"our":[106],"work,":[107],"with":[112],"rigorous":[113],"analyses":[115],"ran":[116],"exponential":[118],"time,":[119],"albeit":[120],"succeeding":[121],"on":[122,153],"larger":[124],"(Li--Qiao,":[128],"FOCS'17;":[129],"Brooksbank--Li--Qiao--Wilson,":[130],"ESA'20;":[131],"Grochow--Qiao--Tang,":[132],"STACS'21).":[133],"These":[134],"reveal":[136],"finer":[138],"landscape":[139],"complexities":[143],"problems,":[146],"providing":[147],"guidance":[148],"cryptographic":[150],"systems":[151],"based":[152],"problems.":[155,173],"technical":[158],"contribution":[159],"is":[160],"introduce":[162],"spectral":[164],"properties":[165],"random":[167,186],"matrices":[168],"into":[169],"This":[174],"leads":[175],"not":[177],"only":[178],"new":[179,183],"but":[181],"also":[182],"questions":[184],"theory":[188],"fields.":[191],"To":[192],"settle":[193],"these":[194],"questions,":[195],"need":[197],"extend":[199],"both":[200],"generating":[202],"function":[203],"approach":[204],"Neumann":[207],"Praeger":[209],"(J.":[210],"London":[211],"Math.":[212,226],"Soc.,":[213,227],"1998)":[214],"characteristic":[217],"sum":[218],"method":[219],"Gorodetsky":[221],"Rodgers":[223],"(Trans.":[224],"Amer.":[225],"2021).":[228]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-03T00:00:00"}