{"id":"https://openalex.org/W7225387252","doi":"https://doi.org/10.5281/zenodo.24000148","title":"Polynomial Length Complexity for the Two-Layer C-RASP Fragment of Chen, Ma and Li","display_name":"Polynomial Length Complexity for the Two-Layer C-RASP Fragment of Chen, Ma and Li","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W7225387252","doi":"https://doi.org/10.5281/zenodo.24000148"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24000148","doi":"https://doi.org/10.5281/zenodo.24000148","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24000148","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24000148","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119746719","display_name":"Kundan Baliga","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Baliga, Kundan","raw_affiliation_strings":["University of Illinois Urbana-Champaign"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5160685850","display_name":"Aiden Xie","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xie, Aiden","raw_affiliation_strings":["Georgia Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5160585827","display_name":"Aditya Byju","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Byju, Aditya","raw_affiliation_strings":["Georgia Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.88919997215271,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.88919997215271,"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/T11567","display_name":"semigroups and automata theory","score":0.0568000003695488,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.018799999728798866,"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/lower-bounds","display_name":"lower bounds","score":0.49399998784065247},{"id":"https://openalex.org/keywords/upper-bounds","display_name":"upper bounds","score":0.7009999752044678},{"id":"https://openalex.org/keywords/computational-learning-theory","display_name":"computational learning theory","score":0.43799999356269836}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7617999911308289},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7515000104904175},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6879000067710876},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.6055999994277954},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.536300003528595},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5058000087738037},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.4894999861717224},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4424000084400177},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.40540000796318054},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3411000072956085},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.29249998927116394},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.26739999651908875},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.26249998807907104}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.5281/zenodo.24000148","doi":"https://doi.org/10.5281/zenodo.24000148","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24000148","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"Preprint"},{"id":"doi:10.5281/zenodo.24000149","doi":"https://doi.org/10.5281/zenodo.24000149","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24000149","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"Preprint"},{"id":"doi:10.5281/zenodo.24020871","doi":"https://doi.org/10.5281/zenodo.24020871","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24020871","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"Preprint"},{"id":"doi:10.5281/zenodo.24021524","doi":"https://doi.org/10.5281/zenodo.24021524","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24021524","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24000148","doi":"https://doi.org/10.5281/zenodo.24000148","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24000148","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W4417095623"],"related_works":["https://openalex.org/W4417095623","https://openalex.org/W2003248189","https://openalex.org/W4298235867","https://openalex.org/W2143728000","https://openalex.org/W109768277","https://openalex.org/W2007444112","https://openalex.org/W1815536947","https://openalex.org/W2289365248","https://openalex.org/W2060763943","https://openalex.org/W2621626451"],"abstract_inverted_index":{"A":[0],"learner":[1,208],"generalizes":[2],"in":[3,45,106],"length":[4,30,38,93,119,159,172],"when":[5],"it":[6],"trains":[7],"on":[8,14,115],"short":[9],"inputs":[10,15],"and":[11,21,59,73,142,177,237,250,266],"is":[12],"correct":[13],"of":[16,32,62,71,78,118,129,160,217,260],"every":[17,41,138,232],"length.":[18],"Chen,":[19],"Ma":[20],"Li":[22],"(ICML":[23],"2025)":[24],"made":[25],"this":[26,107],"quantitative":[27],"through":[28],"the":[29,35,46,79,98,171,200,225,227,244,254,257,261,270],"complexity":[31,173],"a":[33,69,75,214,222,251],"class:":[34],"shortest":[36,152],"input":[37,117,154],"at":[39,64,120,161],"which":[40],"two":[42,104],"distinct":[43],"functions":[44,112],"class":[47],"already":[48],"disagree.":[49],"For":[50],"their":[51],"two-layer":[52,88],"C-RASP":[53,89],"fragment,":[54],"with":[55,134,253],"K":[56,83,145,168,191,234,239],"first-layer":[57],"heads":[58],"integer":[60],"parameters":[61],"size":[63],"most":[65,121],"T,":[66,193],"they":[67],"showed":[68],"bound":[70,77,204,216],"TO(K)":[72],"guessed":[74],"lower":[76,215],"form":[80],"\u03a9(TK)":[81,228],"for":[82,137,165,205,231,238],"\u2264":[84,123,144,146,167,169,190,192,195,197],"\u0398(log":[85,241],"T).":[86,242],"(General":[87],"has":[90,155],"no":[91,131],"computable":[92],"bound;":[94],"these":[95],"results":[96],"concern":[97],"restricted":[99],"fragment.)":[100],"We":[101],"prove":[102],"that":[103,109],"programs":[105],"fragment":[108],"compute":[110],"different":[111],"always":[113],"differ":[114],"an":[116,156],"(B+1)(T+1)(2B\u00b2+T\u00b2+T)+1":[122],"5(K+1)\u00b3T\u2074,":[124],"where":[125],"B=(K+1)T.":[126],"The":[127,179],"exponent":[128],"T":[130,139,147,170,196],"longer":[132],"grows":[133],"K.":[135],"Conversely,":[136],"\u2265":[140,235],"4":[141,194],"2":[143,166],"we":[148,187],"construct":[149],"pairs":[150],"whose":[151],"distinguishing":[153],"exact":[157,185,255],"closed-form":[158],"least":[162],"(1/3)(K\u22121)T\u00b3.":[163],"So":[164],"lies":[174],"between":[175],"\u03a9(KT\u00b3)":[176],"O(K\u00b3T\u2074).":[178],"lower-bound":[180],"construction":[181],"matches":[182],"all":[183,264],"nine":[184],"values":[186],"computed":[188],"(2":[189],"8).":[198],"Corollaries:":[199],"source":[201],"paper's":[202],"\u03b1O(1)":[203],"its":[206,247],"minimum-complexity":[207],"becomes":[209],"O(\u03b1\u2074":[210],"log\u00b3":[211],"\u03b1),":[212],"against":[213],"order":[218],"\u03b13/2;":[219],"read":[220],"as":[221],"statement":[223],"about":[224],"class,":[226],"guess":[229],"fails":[230],"fixed":[233],"5":[236],"=":[240],"Files:":[243],"paper":[245],"(PDF),":[246],"LaTeX":[248],"source,":[249],"supplement":[252],"solvers,":[256],"self-checking":[258],"implementation":[259],"upper-bound":[262],"construction,":[263],"results,":[265],"SHA256SUMS.":[267],"Code":[268],"under":[269],"MIT":[271],"license.":[272],"Version":[273],"1.0":[274],"(2026-11-06):":[275],"first":[276],"release.":[277]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-11-07T00:00:00"}