{"id":"https://openalex.org/W7170173639","doi":"https://doi.org/10.4230/lipics.ccc.2026.8","title":"Efficient Adversaries","display_name":"Efficient Adversaries","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7170173639","doi":"https://doi.org/10.4230/lipics.ccc.2026.8"},"language":"en","primary_location":{"id":"doi:10.4230/lipics.ccc.2026.8","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.ccc.2026.8","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"ConferencePaper"},"type":"conference-paper","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.4230/lipics.ccc.2026.8","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077063223","display_name":"Erfan Khaniki","orcid":"https://orcid.org/0000-0002-5843-7315"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Khaniki, Erfan","raw_affiliation_strings":["University of Oxford, UK"],"raw_orcid":"https://orcid.org/0000-0002-5843-7315","affiliations":[{"raw_affiliation_string":"University of Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059921367","display_name":"J\u00e1n Pich","orcid":"https://orcid.org/0000-0002-2731-1330"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Pich, J\u00e1n","raw_affiliation_strings":["University of Oxford, UK"],"raw_orcid":"https://orcid.org/0000-0002-2731-1330","affiliations":[{"raw_affiliation_string":"University of Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064529000","display_name":"Dmitry Sokolov","orcid":"https://orcid.org/0000-0003-2809-3467"},"institutions":[{"id":"https://openalex.org/I70931966","display_name":"Universit\u00e9 de Montr\u00e9al","ror":"https://ror.org/0161xgx34","country_code":"CA","type":"education","lineage":["https://openalex.org/I70931966"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Sokolov, Dmitry","raw_affiliation_strings":["Universit\u00e9 de Montr\u00e9al, Canada"],"raw_orcid":"https://orcid.org/0000-0003-2809-3467","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Montr\u00e9al, Canada","institution_ids":["https://openalex.org/I70931966"]}]}],"institutions":[],"countries_distinct_count":2,"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":null,"topics":[],"keywords":[{"id":"https://openalex.org/keywords/pigeonhole-principle","display_name":"Pigeonhole principle","score":0.9059000015258789},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.8004999756813049},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7598999738693237},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6672000288963318},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.5838000178337097},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.5627999901771545},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.5551999807357788}],"concepts":[{"id":"https://openalex.org/C171988527","wikidata":"https://www.wikidata.org/wiki/Q188276","display_name":"Pigeonhole principle","level":2,"score":0.9059000015258789},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.8004999756813049},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7598999738693237},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6748999953269958},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6672000288963318},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.5838000178337097},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.5627999901771545},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.5551999807357788},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5450000166893005},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4999000132083893},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.40540000796318054},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39259999990463257},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3522999882698059},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.30390000343322754},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.2750999927520752},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27070000767707825},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.26440000534057617},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2615000009536743}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4230/lipics.ccc.2026.8","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.ccc.2026.8","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"ConferencePaper"}],"best_oa_location":{"id":"doi:10.4230/lipics.ccc.2026.8","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.ccc.2026.8","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"ConferencePaper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"size":[1],"of":[2,10,13,21,33,55,70,95,114,163,176],"Frege":[3,44,140],"proofs":[4],"can":[5],"be":[6],"characterized":[7],"in":[8,103,116,122],"terms":[9],"prover-adversary":[11,22],"games":[12,23],"Pudl\u00e1k":[14],"and":[15,29,72,83,152],"Buss.":[16],"We":[17],"consider":[18],"a":[19,84,133],"generalization":[20],"to":[24,91,158,171],"many":[25],"standard":[26],"proof":[27,36],"systems":[28],"show":[30],"that":[31,106,129],"some":[32],"the":[34,42,48,53,57,62,68,93,104,117,161,173],"major":[35],"complexity":[37],"lower":[38,45,59,75,86,99,135,148],"bounds":[39,149],"such":[40,132],"as":[41],"constant-depth":[43],"bound":[46,60,76,87,136],"for":[47,61,77,138,143,150,165],"pigeonhole":[49,64],"principle":[50,65],"based":[51,66,80],"on":[52,67,81],"method":[54,69],"k-evaluations,":[56],"Resolution":[58],"weak":[63],"pseudo-width":[71],"Razborov\u2019s":[73],"Res(k)":[74],"Nisan-Wigderson":[78],"generators":[79],"expansion":[82],"width":[85],"(which":[88],"is":[89,121,155,169],"used":[90],"derive":[92],"Res(k)-hardness":[94],"formulas":[96,144],"expressing":[97,145],"circuit":[98,147],"bounds)":[100],"are":[101],"constructive":[102,134],"sense":[105],"they":[107],"yield":[108],"efficient":[109],"algorithms":[110],"computing":[111],"winning":[112],"strategies":[113],"adversaries":[115],"generalized":[118],"games.":[119],"This":[120],"contrast":[123],"with":[124],"our":[125],"second":[126],"result":[127],"saying":[128],"if":[130],"(a)":[131],"exists":[137],"Extended":[139],"system":[141],"EF":[142,154],"succinct":[146],"SAT":[151],"(b)":[153],"strong":[156],"enough":[157],"prove":[159],"efficiently":[160],"correctness":[162],"anticheckers":[164],"SAT,":[166],"then":[167],"it":[168],"easy":[170],"separate":[172],"canonical":[174],"pair":[175],"EF.":[177]},"counts_by_year":[],"updated_date":"2026-07-24T06:07:23.975819","created_date":"2026-07-24T00:00:00"}