{"id":"https://openalex.org/W2950615397","doi":"https://doi.org/10.1142/s0219061318500125","title":"Randomized feasible interpolation and monotone circuits with a local oracle","display_name":"Randomized feasible interpolation and monotone circuits with a local oracle","publication_year":2018,"publication_date":"2018-07-06","ids":{"openalex":"https://openalex.org/W2950615397","doi":"https://doi.org/10.1142/s0219061318500125","mag":"2950615397"},"language":"en","primary_location":{"id":"doi:10.1142/s0219061318500125","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061318500125","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1611.08680","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jan Kraj\u00ed\u010dek","orcid":null},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Jan Kraj\u00ed\u010dek","raw_affiliation_strings":["Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovsk\u00e1 83, Prague 8, CZ 186 75, The Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovsk\u00e1 83, Prague 8, CZ 186 75, The Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I21250087"],"apc_list":null,"apc_paid":null,"fwci":0.1897,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.5817137,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","issue":"02","first_page":"1850012","last_page":"1850012"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.7886999845504761,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.7886999845504761,"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/T10142","display_name":"Formal Methods in Verification","score":0.0892999991774559,"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/T10991","display_name":"Game Theory and Voting Systems","score":0.021900000050663948,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6310999989509583},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.5723000168800354},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5580000281333923},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4684999883174896},{"id":"https://openalex.org/keywords/protocol","display_name":"Protocol (science)","score":0.4156999886035919},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.376800000667572},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.36489999294281006}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7056999802589417},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6310999989509583},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5723000168800354},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5580000281333923},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5322999954223633},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4684999883174896},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.4156999886035919},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.376800000667572},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.36489999294281006},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.3424000144004822},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3197000026702881},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.31709998846054077},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.31690001487731934},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0219061318500125","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219061318500125","pdf_url":null,"source":{"id":"https://openalex.org/S29890666","display_name":"Journal of Mathematical Logic","issn_l":"0219-0613","issn":["0219-0613","1793-6691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Logic","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1611.08680","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.08680","pdf_url":"https://arxiv.org/pdf/1611.08680","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1611.08680","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.08680","pdf_url":"https://arxiv.org/pdf/1611.08680","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1575886793","https://openalex.org/W1966278576","https://openalex.org/W1968655942","https://openalex.org/W1982672583","https://openalex.org/W2012476164","https://openalex.org/W2026967932","https://openalex.org/W2029576333","https://openalex.org/W2044095368","https://openalex.org/W2044632231","https://openalex.org/W2078608416","https://openalex.org/W2080045420","https://openalex.org/W2093396771","https://openalex.org/W2125998724","https://openalex.org/W2142326240","https://openalex.org/W2166026605","https://openalex.org/W2908059907","https://openalex.org/W4248733413"],"related_works":[],"abstract_inverted_index":{"The":[0,208,294,363],"feasible":[1,134,211,297],"interpolation":[2,135,212,298],"theorem":[3,136],"for":[4,14,20,202,249,276,372,381,385],"semantic":[5,35,142,173,218,308],"derivations":[6,36,143,174,225],"from":[7,32,94],"[J.":[8],"Kraj\u00ed\u010dek,":[9],"Interpolation":[10],"theorems,":[11],"lower":[12,274,370,379],"bounds":[13,380],"proof":[15,157,277,302,333],"systems,":[16],"and":[17,52,81,115,253,304,343,351],"independence":[18],"results":[19],"bounded":[21],"arithmetic,":[22],"J.":[23,335,357],"Symbolic":[24,336,358],"Logic":[25,127,337,359],"62(2)":[26],"(1997)":[27,69],"457\u2013486]":[28],"allows":[29],"to":[30,137,153,167,199,271,300,306,314,344,377],"derive":[31],"some":[33],"short":[34,217],"(e.g.":[37,152],"in":[38,64,228],"resolution)":[39],"of":[40,43,67,141,147,172,184,224,232,235,320,329,348,354],"the":[41,65,71,79,105,108,116,133,145,154,165,185,229,233,260,268,330],"disjointness":[42,234],"two":[44,261],"[Formula:":[45,49,53,74,91,95,99,112,203,236,239,250,279,291],"see":[46,50,54,75,92,96,100,113,204,237,240,251,280,292],"text]":[47,51,55,76,93,101,114,205,241,252,281],"sets":[48],"a":[56,83,87,124,138,148,168,192,216,221,245,255,273,326],"small":[57,88,246,256,315],"communication":[58,150,200],"protocol":[59,63,84,106,248],"(a":[60],"general":[61],"dag-like":[62],"sense":[66],"Kraj\u00ed\u010dek":[68,121,321],"computing":[70],"Karchmer\u2013Wigderson":[72,110],"multi-function":[73,111],"associated":[77],"with":[78,191,283],"sets,":[80],"such":[82],"further":[85],"yields":[86,244],"circuit":[89,118,187],"separating":[90,259],"text].":[97,293],"When":[98],"is":[102,119,265,375],"closed":[103,242],"upwards,":[104,243],"computes":[107],"monotone":[109,186,189,257,386],"resulting":[117],"monotone.":[120],"[Interpolation":[122],"by":[123,175,267,286],"game,":[125],"Math.":[126],"Quart.":[128],"44(4)":[129],"(1998)":[130,339],"450\u2013458]":[131],"extended":[132],"larger":[139,170,226],"class":[140,171,223],"using":[144],"notion":[146],"real":[149],"complexity":[151],"cutting":[155,311,331],"planes":[156,312,332],"system":[158,278,303],"CP).":[159],"In":[160],"this":[161,301,373],"paper,":[162],"we":[163],"generalize":[164],"method":[166,364],"still":[169],"allowing":[176],"randomized":[177,210,247,296,382],"protocols.":[178],"We":[179],"also":[180,305],"introduce":[181],"an":[182],"extension":[183,328],"model,":[188],"circuits":[190],"local":[193],"oracle":[194],"(CLOs),":[195],"that":[196,215],"does":[197,365],"correspond":[198],"protocols":[201,383],"making":[206],"errors.":[207],"new":[209,295],"thus":[213],"shows":[214],"derivation":[219],"(from":[220],"certain":[222],"than":[227],"original":[230],"method)":[231],"text],":[238],"hence":[254],"CLO":[258],"sets.":[262],"This":[263],"research":[264],"motivated":[266],"open":[269],"problem":[270],"establish":[272,378],"bound":[275],"operating":[282],"clauses":[284],"formed":[285],"linear":[287],"Boolean":[288],"functions":[289],"over":[290,318],"applies":[299],"(the":[307],"versions":[309],"of)":[310],"CP,":[313],"width":[316],"resolution":[317,346],"CP":[319],"[Discretely":[322],"ordered":[323],"modules":[324],"as":[325],"first-order":[327],"system,":[334],"63(4)":[338],"1582\u20131596]":[340],"(system":[341],"R(CP))":[342],"random":[345],"RR":[347],"Buss,":[349],"Kolodziejczyk":[350],"Thapen":[352],"[Fragments":[353],"approximate":[355],"counting,":[356],"79(2)":[360],"(2014)":[361],"496\u2013525].":[362],"not":[366],"yield":[367],"yet":[368],"lengths-of-proofs":[369],"bounds;":[371],"it":[374],"necessary":[376],"or":[384],"CLOs.":[387]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2019-06-27T00:00:00"}
