{"id":"https://openalex.org/W7166568719","doi":"https://doi.org/10.48550/arxiv.2606.27931","title":"Provable Reductions in TFNP","display_name":"Provable Reductions in TFNP","publication_year":2026,"publication_date":"2026-06-26","ids":{"openalex":"https://openalex.org/W7166568719","doi":"https://doi.org/10.48550/arxiv.2606.27931"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.27931","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27931","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.27931","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082438935","display_name":"Noah Fleming","orcid":"https://orcid.org/0000-0002-8636-1290"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fleming, Noah","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120681431","display_name":"Stefan Grosser","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Grosser, Stefan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003318200","display_name":"Toniann Pitassi","orcid":"https://orcid.org/0000-0002-8668-2174"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pitassi, Toniann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5021914150","display_name":"Robert Robere","orcid":"https://orcid.org/0000-0002-6065-6023"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robere, Robert","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.2646999955177307,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.2646999955177307,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.19930000603199005,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.1914999932050705,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/proof-complexity","display_name":"Proof complexity","score":0.7962999939918518},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6572999954223633},{"id":"https://openalex.org/keywords/structural-proof-theory","display_name":"Structural proof theory","score":0.5504999756813049},{"id":"https://openalex.org/keywords/sequent","display_name":"Sequent","score":0.515500009059906},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.49300000071525574},{"id":"https://openalex.org/keywords/analytic-proof","display_name":"Analytic proof","score":0.4851999878883362},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.482699990272522},{"id":"https://openalex.org/keywords/direct-proof","display_name":"Direct proof","score":0.47429999709129333},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4496999979019165}],"concepts":[{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.7962999939918518},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6915000081062317},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6572999954223633},{"id":"https://openalex.org/C195653647","wikidata":"https://www.wikidata.org/wiki/Q7625047","display_name":"Structural proof theory","level":4,"score":0.5504999756813049},{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.515500009059906},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.49300000071525574},{"id":"https://openalex.org/C135754263","wikidata":"https://www.wikidata.org/wiki/Q4751136","display_name":"Analytic proof","level":3,"score":0.4851999878883362},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4846999943256378},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.482699990272522},{"id":"https://openalex.org/C161505775","wikidata":"https://www.wikidata.org/wiki/Q3240280","display_name":"Direct proof","level":2,"score":0.47429999709129333},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4496999979019165},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.4050999879837036},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3953999876976013},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.39399999380111694},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C74640108","wikidata":"https://www.wikidata.org/wiki/Q1372900","display_name":"Propositional formula","level":5,"score":0.3479999899864197},{"id":"https://openalex.org/C16221470","wikidata":"https://www.wikidata.org/wiki/Q846564","display_name":"Conjunctive normal form","level":2,"score":0.32330000400543213},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.32030001282691956},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.3133000135421753},{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.310699999332428},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.29989999532699585},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.29989999532699585},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.29429998993873596},{"id":"https://openalex.org/C111404639","wikidata":"https://www.wikidata.org/wiki/Q376166","display_name":"Cut-elimination theorem","level":4,"score":0.2727999985218048},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.26159998774528503},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.26019999384880066},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.2572000026702881},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.2554999887943268}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.27931","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27931","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.27931","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27931","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"},"sustainable_development_goals":[{"score":0.7464354634284973,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,117,131,179,187],"introduce":[1],"a":[2,19,22,30,79,91,100,126,170,195,222,232,260],"new":[3],"family":[4],"of":[5,21,64,73,103,106,164,177],"propositional":[6,62],"proof":[7,46,107,120,148,167,172,233,251],"systems,":[8],"denoted":[9],",":[10,122],"for":[11,88,129,182,249],"an":[12,43,165],"arbitrary":[13],"TFNP":[14,92,115,184],"search":[15,36,86,196,263],"problem":[16,37,87,128,197,223,264],"$R$.":[17,186],"Informally,":[18],"refutation":[20],"CNF":[23],"formula":[24],"$F$":[25],"in":[26,55,67,78,90,200,229],"is":[27,50,125,134,160,199,203,237,255,259,271,288],"given":[28],"by":[29,70,169],"polynomial-time":[31,261],"reduction":[32,49],"from":[33],"the":[34,48,61,85,104,119,138,145,161,175],"false-clause":[35],"$Search_F$":[38],"to":[39,95,113,137,144,206,210,220,227,239,274,291],"$R$,":[40],"combined":[41],"with":[42],"Extended":[44,243],"Frege":[45],"that":[47,133,189,194,216,236,248,270,287],"correct.":[51],"These":[52],"are":[53,60,99,157],"motivated":[54],"two":[56,284],"ways:":[57],"1.":[58],"They":[59,98],"translations":[63],"witnessing":[65],"theorems":[66],"bounded":[68],"arithmetic,":[69],"which":[71,159,214,254],"proofs":[72],"$\\forall":[74],"\u03a3^b_1$":[75],"formulas":[76],"$\u03d5$":[77,89],"theory":[80],"$T$":[81],"imply":[82],"algorithms":[83],"solving":[84],"class":[93],"corresponding":[94],"$T$.":[96],"2.":[97],"white-box":[101],"analogue":[102],"characterizations":[105],"systems":[108],"using":[109],"decision":[110],"tree":[111],"reductions":[112,219],"black-box":[114],"problems.":[116],"consider":[118,181],"system":[121,149,168,173,234,252],"where":[123],"Iter":[124],"complete":[127],"PLS.":[130],"prove":[132,193],"polynomially":[135,204,272,289],"equivalent":[136,205,273,290],"sequent":[139],"calculus":[140],"$G_1$,":[141],"and":[142,154,281],"also":[143,180],"implicit":[146,166],"Resolution":[147],"[EF,":[150,155,279],"Resolution].":[151],"Hence":[152],"$G_1$":[153],"Resolution]":[156,280],"equivalent,":[158],"first":[162],"characterization":[163],"classical":[171],"beyond":[174],"work":[176],"Wang.":[178],"general":[183],"relations":[185],"observe":[188],"if":[190],"EF":[191],"can":[192],"$R$":[198],"FP,":[201,230],"then":[202],"EF.":[207],"This":[208],"contrasts":[209],"our":[211,283],"above":[212],"result,":[213],"shows":[215,286],"Extended-Frege":[217],"provable":[218],"$Iter$,":[221],"widely":[224],"believed":[225,238],"not":[226],"be":[228,240],"yields":[231],"($G_1$)":[235],"stronger":[241],"than":[242],"Frege.":[244],"Finally,":[245],"we":[246],"show":[247],"any":[250],"$P$":[253],"sufficiently":[256],"strong,":[257],"there":[258],"computable":[262],"$R_P":[265],"\\in":[266],"$":[267],"FP":[268],"such":[269],"$P$.":[275],"Letting":[276],"$P":[277],"=$":[278],"combining":[282],"results":[285],".":[292]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-30T00:00:00"}