{"id":"https://openalex.org/W3023658018","doi":"https://doi.org/10.1145/3357713.3384251","title":"Unexpected hardness results for Kolmogorov complexity under uniform reductions","display_name":"Unexpected hardness results for Kolmogorov complexity under uniform reductions","publication_year":2020,"publication_date":"2020-06-06","ids":{"openalex":"https://openalex.org/W3023658018","doi":"https://doi.org/10.1145/3357713.3384251","mag":"3023658018"},"language":"en","primary_location":{"id":"doi:10.1145/3357713.3384251","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3357713.3384251","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062484134","display_name":"Shuichi Hirahara","orcid":"https://orcid.org/0000-0002-3101-446X"},"institutions":[{"id":"https://openalex.org/I184597095","display_name":"National Institute of Informatics","ror":"https://ror.org/04ksd4g47","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I184597095","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Shuichi Hirahara","raw_affiliation_strings":["National Institute of Informatics, Japan","National Institute of Informatics, JAPAN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Institute of Informatics, Japan","institution_ids":["https://openalex.org/I184597095"]},{"raw_affiliation_string":"National Institute of Informatics, JAPAN","institution_ids":["https://openalex.org/I184597095"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5062484134"],"corresponding_institution_ids":["https://openalex.org/I184597095"],"apc_list":null,"apc_paid":null,"fwci":0.3375,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.4302226,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"27","issue":null,"first_page":"1038","last_page":"1051"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9976999759674072,"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":0.9976999759674072,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9902999997138977,"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/T10237","display_name":"Cryptography and Data Security","score":0.9869999885559082,"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/kolmogorov-complexity","display_name":"Kolmogorov complexity","score":0.8819378614425659},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6895508766174316},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6190732717514038},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.5882972478866577},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5794348120689392},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5552680492401123},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.5396933555603027},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5356724858283997},{"id":"https://openalex.org/keywords/dtime","display_name":"DTIME","score":0.509739339351654},{"id":"https://openalex.org/keywords/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.48008495569229126},{"id":"https://openalex.org/keywords/communication-complexity","display_name":"Communication complexity","score":0.4596412479877472},{"id":"https://openalex.org/keywords/structural-complexity-theory","display_name":"Structural complexity theory","score":0.4515843987464905},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.42861148715019226},{"id":"https://openalex.org/keywords/kolmogorov-structure-function","display_name":"Kolmogorov structure function","score":0.4153746962547302},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4112316370010376},{"id":"https://openalex.org/keywords/turing-machine","display_name":"Turing machine","score":0.35060638189315796},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14390018582344055},{"id":"https://openalex.org/keywords/universal-turing-machine","display_name":"Universal Turing machine","score":0.0946313738822937}],"concepts":[{"id":"https://openalex.org/C2779341405","wikidata":"https://www.wikidata.org/wiki/Q1456811","display_name":"Kolmogorov complexity","level":2,"score":0.8819378614425659},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6895508766174316},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6190732717514038},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.5882972478866577},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5794348120689392},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5552680492401123},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.5396933555603027},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5356724858283997},{"id":"https://openalex.org/C15547884","wikidata":"https://www.wikidata.org/wiki/Q1155831","display_name":"DTIME","level":5,"score":0.509739339351654},{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.48008495569229126},{"id":"https://openalex.org/C179145077","wikidata":"https://www.wikidata.org/wiki/Q5154130","display_name":"Communication complexity","level":2,"score":0.4596412479877472},{"id":"https://openalex.org/C131583701","wikidata":"https://www.wikidata.org/wiki/Q7625020","display_name":"Structural complexity theory","level":4,"score":0.4515843987464905},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.42861148715019226},{"id":"https://openalex.org/C15995199","wikidata":"https://www.wikidata.org/wiki/Q5805968","display_name":"Kolmogorov structure function","level":3,"score":0.4153746962547302},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4112316370010376},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.35060638189315796},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14390018582344055},{"id":"https://openalex.org/C131671149","wikidata":"https://www.wikidata.org/wiki/Q2703890","display_name":"Universal Turing machine","level":4,"score":0.0946313738822937},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3357713.3384251","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3357713.3384251","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"mag:3023658018","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/eccc/eccc27.html#Hirahara20","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Electron. Colloquium Comput. Complex.","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7167969490","display_name":"Quantum Algorithms for Large-Scale Quantum Computers: New Horizons and Applications","funder_award_id":"20H04139","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8027246332","display_name":"Computational Complexity of Minimum Description Size Problems","funder_award_id":"18H04090","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W159595461","https://openalex.org/W1831013898","https://openalex.org/W1850905020","https://openalex.org/W1901622511","https://openalex.org/W1966819396","https://openalex.org/W1971142267","https://openalex.org/W1990663377","https://openalex.org/W1996484429","https://openalex.org/W2004130530","https://openalex.org/W2028930979","https://openalex.org/W2036265926","https://openalex.org/W2042851910","https://openalex.org/W2043280328","https://openalex.org/W2048284438","https://openalex.org/W2056994701","https://openalex.org/W2062855793","https://openalex.org/W2072181151","https://openalex.org/W2078472124","https://openalex.org/W2083820240","https://openalex.org/W2086059606","https://openalex.org/W2089272132","https://openalex.org/W2108585502","https://openalex.org/W2109677942","https://openalex.org/W2112243290","https://openalex.org/W2125495920","https://openalex.org/W2128322939","https://openalex.org/W2151306421","https://openalex.org/W2289098369","https://openalex.org/W2402456376","https://openalex.org/W2608011726","https://openalex.org/W2615716136","https://openalex.org/W2621027562","https://openalex.org/W2787265165","https://openalex.org/W2794018377","https://openalex.org/W2888575364","https://openalex.org/W2947191600","https://openalex.org/W2998808137","https://openalex.org/W3003959968","https://openalex.org/W4205550388","https://openalex.org/W4256317935","https://openalex.org/W6632664761","https://openalex.org/W6639611802","https://openalex.org/W6679636167","https://openalex.org/W6693488411","https://openalex.org/W6713199455","https://openalex.org/W6736393795","https://openalex.org/W6773271504"],"related_works":["https://openalex.org/W3034183797","https://openalex.org/W1756533857","https://openalex.org/W3168614261","https://openalex.org/W1542401186","https://openalex.org/W2469381561","https://openalex.org/W2273702009","https://openalex.org/W2279489453","https://openalex.org/W1966098169","https://openalex.org/W2753256758","https://openalex.org/W2773570193","https://openalex.org/W2178059285","https://openalex.org/W3157102507","https://openalex.org/W2951756435","https://openalex.org/W2465024128","https://openalex.org/W1987681136","https://openalex.org/W2099020009","https://openalex.org/W275231650","https://openalex.org/W1511844090","https://openalex.org/W2964773335","https://openalex.org/W3127217102"],"abstract_inverted_index":{"Hardness":[0],"of":[1,6,17,25,30,48,71,125,139,147,161],"computing":[2,49],"the":[3,31,67,123,128,137],"Kolmogorov":[4,26,50],"complexity":[5,27,35,51],"a":[7,14,143,148,152],"given":[8],"string":[9],"is":[10,28,64,74,142],"closely":[11],"tied":[12],"to":[13,60,98],"security":[15,145],"proof":[16,43,146],"hitting":[18],"set":[19,68],"generators,":[20],"and":[21,87,121,163],"thus":[22],"understanding":[23],"hardness":[24,47,119],"one":[29],"central":[32],"questions":[33],"in":[34],"theory.":[36],"In":[37],"this":[38],"paper,":[39],"we":[40],"develop":[41],"new":[42,144],"techniques":[44],"for":[45],"showing":[46],"under":[52,76,127],"surprisingly":[53],"efficient":[54],"reductions,":[55,79],"which":[56,95,115,156],"were":[57],"previously":[58],"conjectured":[59,97],"be":[61,99],"impossible.":[62],"It":[63],"known":[65],"that":[66,88,107,131],"R":[69,84,92,112],"K":[70,85,93,113],"Kolmogorov-random":[72],"strings":[73],"PSPACE-hard":[75],"polynomial-time":[77],"Turing":[78],"i.e.,":[80],"PSPACE":[81],"\u2282":[82,90,110],"P":[83,111],",":[86,94,114],"NEXP":[89],"NP":[91,109,133],"was":[96],"tight":[100],"by":[101],"Allender":[102,126],"(CiE":[103],"2012).":[104],"We":[105],"prove":[106],"EXP":[108,132],"simultaneously":[116],"improves":[117],"these":[118],"results":[120,141],"refutes":[122],"conjecture":[124],"plausible":[129],"assumption":[130],"\u2260":[134],"NEXP.":[135],"At":[136],"core":[138],"our":[140],"pseudorandom":[149],"generator":[150],"via":[151],"black-box":[153],"uniform":[154],"reduction,":[155],"overcomes":[157],"an":[158],"impossibility":[159],"result":[160],"Gutfreund":[162],"Vadhan":[164],"(RANDOM/APPROX":[165],"2008).":[166]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-24T07:32:12.397491","created_date":"2025-10-10T00:00:00"}
